Relevant bibliographies by topics / Fractional partial derivatives

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Fractional partial derivatives'

Author: Grafiati
Published: 7 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Fractional partial derivatives"

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Chii-Huei, Yu. "Evaluating the Fractional Partial Derivatives of Some Two-Variables Fractional Functions." International Journal of Computer Science and Information Technology Research 12, no. 4 (2024): 5–11. https://doi.org/10.5281/zenodo.13959773.

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<strong>Abstract:</strong> In this paper, based on Jumarie&rsquo;s modified Riemann-Liouville (R-L) fractional derivative and a new multiplication of fractional analytic functions, we can find the fractional partial derivatives of some two-variables fractional functions. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie&rsquo;s modified R-L fractional derivative, new multiplication, fractional analytic functions, fractional partial derivatives, two-variables fractional functions. <strong>Title:</strong> Evaluating the Fractional Partial Derivatives of Some Two-Variables Fractional Functions <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Computer Science and Information Technology Research</strong> <strong>ISSN 2348-1196 (print), ISSN 2348-120X (online)</strong> <strong>Vol. 12, Issue 4, October 2024 - December 2024</strong> <strong>Page No: 5-11</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 21-October-2024</strong> <strong>DOI: https://doi.org/10.5281/zenodo.13959773</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/evaluating-the-fractional-partial-derivatives-of-some-two-variables-fractional-functions</strong>
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Li, Changpin, Deliang Qian, and YangQuan Chen. "On Riemann-Liouville and Caputo Derivatives." Discrete Dynamics in Nature and Society 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/562494.

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Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in science and engineering.
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Hu, Langhua, Duan Chen, and Guo-Wei Wei. "High-order fractional partial differential equation transform for molecular surface construction." Computational and Mathematical Biophysics 1 (December 20, 2012): 1–25. http://dx.doi.org/10.2478/mlbmb-2012-0001.

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AbstractFractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.
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Kirianova, Ludmila Vladimirovna. "The Boundary Value Problem with Stationary Inhomogeneities for a Hyperbolic-Type Equation with a Fractional Derivative." Axioms 11, no. 5 (2022): 207. http://dx.doi.org/10.3390/axioms11050207.

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The paper presents an analytical solution of a partial differential equation of hyperbolic-type, containing both second-order partial derivatives and fractional derivatives of order below the second. Examples of applying the solution of a boundary value problem with stationary inhomogeneities for a hyperbolic-type equation with a fractional derivative in modeling the behavior of polymer concrete under the action of loads are considered.
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Agarwal, Ravi P., Snezhana Hristova, and Donal O’Regan. "Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations." Fractal and Fractional 7, no. 1 (2023): 80. http://dx.doi.org/10.3390/fractalfract7010080.

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In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of derivative generalizes several known types in the literature for fractional derivatives such as the Caputo fractional derivative. Thus, the obtained results additionally generalize some known models in the literature. The long term behavior of the solution of the model when the time is increasing without a bound is studied and sufficient conditions for approaching zero are obtained. Lyapunov functions defined as a sum of squares with their generalized proportional Caputo fractional derivatives are applied and a comparison result for a scalar linear generalized proportional Caputo fractional differential equation with several constant delays is presented. Lyapunov functions and the comparison principle are then combined to establish our main results.
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Elbeleze, Asma Ali, Adem Kılıçman, and Bachok M. Taib. "Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/543848.

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We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.
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Ali, Khalid K., F. E. Abd Elbary, Mohamed S. Abdel-Wahed, M. A. Elsisy, and Mourad S. Semary. "Solving Nonlinear Fractional PDEs with Applications to Physics and Engineering Using the Laplace Residual Power Series Method." International Journal of Differential Equations 2023 (December 27, 2023): 1–19. http://dx.doi.org/10.1155/2023/1240970.

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The Laplace residual power series (LRPS) method uses the Caputo fractional derivative definition to solve nonlinear fractional partial differential equations. This technique has been applied successfully to solve equations such as the fractional Kuramoto–Sivashinsky equation (FKSE) and the fractional generalized regularized long wave equation (GRLWE). By transforming the equation into the Laplace domain and replacing fractional derivatives with integer derivatives, the LRPS method can solve the resulting equation using a power series expansion. The resulting solution is accurate and convergent, as demonstrated in this paper by comparing it with other analytical methods. The LRPS approach offers both computational efficiency and solution accuracy, making it an effective technique for solving nonlinear fractional partial differential equations (NFPDEs). The results are presented in the form of graphs for various values of the order of the fractional derivative and time, and the essential objective is to reduce computation effort.
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Lazopoulos, Konstantinos A. "On Λ-Fractional Differential Equations". Foundations 2, № 3 (2022): 726–45. http://dx.doi.org/10.3390/foundations2030050.

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Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the Λ-fractional derivative conforms to all prerequisites demanded by differential topology. Hence, the various mathematical forms, including those derivatives, do not lack the mathematical accuracy or defects of the well-known fractional derivatives. A summary of the Λ-fractional analysis is presented with its influence on the sources of differential equations, such as fractional differential geometry, field theorems, and calculus of variations. Λ-fractional ordinary and partial differential equations will be discussed.
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Zainal, Nor Hafizah, and Adem Kılıçman. "Solving Fractional Partial Differential Equations with Corrected Fourier Series Method." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/958931.

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The corrected Fourier series (CFS) is proposed for solving partial differential equations (PDEs) with fractional time derivative on a finite domain. In the previous work, we have been solving partial differential equations by using corrected Fourier series. The fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions.
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Alharthi, Nadiyah Hussain, Abdon Atangana, and Badr S. Alkahtani. "Numerical analysis of some partial differential equations with fractal-fractional derivative." AIMS Mathematics 8, no. 1 (2022): 2240–56. http://dx.doi.org/10.3934/math.2023116.

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&lt;abstract&gt; &lt;p&gt;In this study, we expanded the partial differential equation framework to which fractal-fractional differentiation can be applied. For this, we employed the generalized Mittag-Leffler function, and the fractal-fractional derivatives based on the power-law kernel. A general partial differential equation with the fractal-fractional derivative, the power law kernel and the generalized Mittag-Leffler function was thoroughly examined. There is almost no numerical scheme for solving partial differential equations with fractal-fractional derivatives, as less investigation has been done in this direction in the last decades. In this work, therefore, we shall attempt to provide a numerical method that might be used to solve these equations in each circumstance. The heat equation was taken into consideration for the application and numerically solved using a few simulations for various values of fractional and fractal orders. It is observed that, when the fractal order is 1, one obtains fractional partial differential equations which have been known to replicate nonlocal behaviors. Meanwhile, if the fractional order is 1, one obtains fractal-partial differential equations. Thus, when the fractional order and fractal dimension are different from zero, nonlocal processes with similar features are developed.&lt;/p&gt; &lt;/abstract&gt;
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Dissertations / Theses on the topic "Fractional partial derivatives"

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Rakotonasy, Solonjaka Hiarintsoa. "Modèle fractionnaire pour la sous-diffusion : version stochastique et edp." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00839892.

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Ce travail a pour but de proposer des outils visant 'a comparer des résultats exp'erimentaux avec des modèles pour la dispersion de traceur en milieu poreux, dans le cadre de la dispersion anormale.Le "Mobile Immobile Model" (MIM) a été à l'origine d'importants progrès dans la description du transport en milieu poreux, surtout dans les milieux naturels. Ce modèle généralise l'quation d'advection-dispersion (ADE) e nsupposant que les particules de fluide, comme de solut'e, peuvent ˆetre immo-bilis'ees (en relation avec la matrice solide) puis relˆachées, le piégeage et le relargage suivant de plus une cin'etique d'ordre un. Récemment, une version stochastique de ce modèle a 'eté proposée. Malgré de nombreux succès pendant plus de trois décades, le MIM reste incapable de repr'esenter l''evolutionde la concentration d'un traceur dans certains milieux poreux insaturés. Eneffet, on observe souvent que la concentration peut d'ecroˆıtre comme unepuissance du temps, en particulier aux grands temps. Ceci est incompatible avec la version originale du MIM. En supposant une cinétique de piégeage-relargage diff'erente, certains auteurs ont propos'e une version fractionnaire,le "fractal MIM" (fMIM). C'est une classe d''equations aux d'eriv'ees par-tielles (e.d.p.) qui ont la particularit'e de contenir un op'erateur int'egral li'e'a la variable temps. Les solutions de cette classe d'e.d.p. se comportentasymptotiquement comme des puissances du temps, comme d'ailleurs cellesde l''equation de Fokker-Planck fractionnaire (FFPE). Notre travail fait partie d'un projet incluant des exp'eriences de tra¸cageet de vélocimétrie par R'esistance Magn'etique Nucl'eaire (RMN) en milieuporeux insatur'e. Comme le MIM, le fMIM fait partie des mod'eles ser-vant 'a interpréter de telles exp'eriences. Sa version "e.d.p." est adapt'eeaux grandeurs mesur'ees lors d'exp'eriences de tra¸cage, mais est peu utile pour la vélocimétrie RMN. En effet, cette technique mesure la statistiquedes d'eplacements des mol'ecules excit'ees, entre deux instants fixés. Plus précisément, elle mesure la fonction caractéristique (transform'ee de Fourier) de ces d'eplacements. Notre travail propose un outil d'analyse pour ces expériences: il s'agit d'une expression exacte de la fonction caract'eristiquedes d'eplacements de la version stochastique du mod'ele fMIM, sans oublier les MIM et FFPE. Ces processus sont obtenus 'a partir du mouvement Brown-ien (plus un terme convectif) par des changement de temps aléatoires. Ondit aussi que ces processus sont des mouvement Browniens, subordonnéspar des changements de temps qui sont eux-mˆeme les inverses de processusde L'evy non d'ecroissants (les subordinateurs). Les subordinateurs associés aux modèles fMIM et FFPE sont des processus stables, les subordinateursassoci'es au MIM sont des processus de Poisson composites. Des résultatsexp'erimenatux tr'es r'ecents on sugg'er'e d''elargir ceci 'a des vols de L'evy (plusg'en'eraux que le mouvement Brownien) subordonnés aussi.Le lien entre les e.d.p. fractionnaires et les mod'eles stochastiques pourla sous-diffusion a fait l'objet de nombreux travaux. Nous contribuons 'ad'etailler ce lien en faisant apparaˆıtre les flux de solut'e, en insistant sur une situation peu 'etudiée: nous examinons le cas o'u la cinétique de piégeage-relargage n'est pas la mˆeme dans tout le milieu. En supposant deux cinétiques diff'erentes dans deux sous-domaines, nous obtenons une version du fMIMavec un opérateur intégro-diff'erentiel li'e au temps, mais dépendant de la position.Ces r'esultats sont obtenus au moyen de raisonnements, et sont illustrés par des simulations utilisant la discrétisation d'intégrales fractionnaires etd'e.d.p. ainsi que la méthode de Monte Carlo. Ces simulations sont en quelque sorte des preuves numériques. Les outils sur lesquels elles s'appuient sont présentés aussi.
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(10734243), Attila Lendek. "TIME-VARYING FRACTIONAL-ORDER PID CONTROL FOR MITIGATION OF DERIVATIVE KICK." Thesis, 2021.

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<div>In this thesis work, a novel approach for the design of a fractional order proportional integral</div><div>derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller</div><div>to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The</div><div>voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a</div><div>derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is</div><div>left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to</div><div>take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains</div><div>a fast system response and signi?cantly reduces the voltage spike at the controller output. The time-varying</div><div>FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm</div><div>(GA) to ?nd the optimum constants and time-varying parameters. The improved control performance is</div><div>validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID</div><div>controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created</div><div>for comparison with all three PID gain constants replaced by the optimized time functions. The simulation</div><div>results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage</div><div>spike at the controller output but also is also able to keep approximately the same characteristics of the system</div><div>response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation</div><div>block between the controller output and the plant still performs best according to system overshoot, rise time,</div><div>and settling time.</div>
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Paiva, Maria Inês Patrício. "Métodos numéricos para modelos de preços de opções baseados em processos de Lévy." Master's thesis, 2021. http://hdl.handle.net/10316/95508.

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Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia<br>O modelo de Black-Scholes foi um dos primeiros modelos de preços de opções europeias a ser aceite. Ainda hoje, este modelo desempenha um papel fundamental na previsão dos preços de uma opção, devido à facilidade que existe na sua implementação e ao facto da sua fórmula só depender de um único parâmetro não observável. No entanto, também apresenta algumas limitações, por causa de suposições estritas ou pouco realistas que lhe estão subjacentes. Daí que, foram desenvolvidos outros modelos que contornassem estas limitações, como é o caso do modelo de preços de opções baseado num processo de Lévy. Nesta dissertação, iremos deduzir equações diferencias representativas de cada um destes modelos e iremos estudar em pormenor a equação do modelo de preços de opções baseado num processo de Lévy. A equação diferencial representativa destes modelos baseados em processos de Lévy, é uma equação diferencial parcial fracionária por conter o operador fracionário de Riemann Liouville. As metodologias usadas na resolução desta equação, requerem que encontremos uma aproximação para este operador, de forma a que, possamos aplicar métodos numéricos. Assim, por um resultado teórico, que relaciona o operador fracionário de Riemann-Liouville com o operador fracionário de Grünwald-Letnikov, somos capazes de discretizar uma equação segundo o método implícito de Euler e segundo o método de Crank-Nicolson. De forma a que, possamos posteriormente, encontrar soluções numéricas para estes modelos de preços de opções de estilo europeu, tendo em conta determinadas condições de fronteira, e retirar conclusões quanto às propriedades de cada método numérico. Para além disso, pela introdução de um método de extrapolação, pretendemos diminuir os erros de aproximação e aumentar a ordem de convergência, obtendo resultados computacionais melhorados. Deste modo, este trabalho expressa bem como os diferentes ramos da matemática se conjugam, para solucionar problemas cada vez mais complexos, impostos pelos desafios dos mercados financeiros.<br>The Black-Scholes model was one of the first european-style option pricing models to be accepted. Even today, this model plays a fundamental role in predicting the prices of an option, due to the easiness that exists in its implementation and the fact that its formula only depends on a single unobservable parameter. However, it also has some limitations, because of the strict or unrealistic assumptions that underlie it. Hence, other models were developed to circumvent these limitations, such as the option pricing model based on a Lévy process. In this dissertation, we will deduce representative differential equations for each one of these models, and we will study, in detail, the equation of the option pricing model based on a Lévy process. The differential equation representing these models based on Lévy processes is a fractional partial differential equation because of the Riemann-Liouville fractional operator. The methodologies used in solving this equation, require us to find an approximation for this operator, so that we can apply numerical methods. Thus, by a theoretical result, which relates the Riemann-Liouville fractional operator with the Grünwald-Letnikov fractional operator, we are able to discretize an equation according to the implicit Euler method and according to the Crank-Nicolson method. So that we can later find numerical solutions for these european -style option pricing models, taking into account certain boundary conditions, and withdraw conclusions about the properties of each numerical method. Furthermore, by introducing an extrapolation method, we intend to reduce approximation errors and increase the order of convergence, obtaining improved computational results. In this way, this work expresses well how the different branches of mathematics come together to solve increasingly complex problems, imposed by the challenges of the financial markets.
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Book chapters on the topic "Fractional partial derivatives"

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Salehi, Younes, and William E. Schiesser. "Variation in the Order of the Fractional Derivatives." In Numerical Integration of Space Fractional Partial Differential Equations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-031-02411-5_2.

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Krempl, Peter W. "Semi-integrals and Semi-derivatives in Particle Physics." In Advances in Fractional Calculus. Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6042-7_10.

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Waadeland, Haakon. "A note on partial derivatives of continued fractions." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075944.

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Alisultanov, Z. Z., A. M. Agalarov, A. A. Potapov, and G. B. Ragimkhanov. "Some Applications of Fractional Derivatives in Many-Particle Disordered Large Systems." In Fractional Dynamics, Anomalous Transport and Plasma Science. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04483-1_7.

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Hemalatha, S., and S. Margret Anouncia. "Partial Fractional Derivative (PFD) based Texture Analysis Model for Medical Image Segmentation." In Knowledge Computing and Its Applications. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-6680-1_11.

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Toma, Theodora, Stefan Pusca, and Cristian Morarescu. "Simulating Superradiant Laser Pulses Using Partial Fraction Decomposition and Derivative Procedures." In Computational Science and Its Applications - ICCSA 2006. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11751540_83.

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Zhang, Yingkai, and Weitao Yang. "Perspective on “Density-functional theory for fractional particle number: derivative discontinuities of the energy”." In Theoretical Chemistry Accounts. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-10421-7_57.

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Oliva-Sanchez, Pedro, Ruben Aguilar-Marquez, Javier Alejandro Pérez-Garza, Edelmiro Leal-Fernandez, and Servando Lopez-Aguayo. "Analysis of the Fractional Schrödinger Equation with Free Particle Potential in One Dimension with Caputo and Caputo-Fabrizio Derivatives." In Modeling and Optimization in Science and Technologies. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-83989-4_10.

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SINGH, PRABAL PRATAP, OMENDRA SINGH, and SEEMA RAGHAV. "REDUCED DIFFERENTIAL TRANSFORM METHOD FOR TIME FRACTIONAL NONLINEAR PDES: MATHEMATICAL FRAMEWORK AND COMPUTATIONAL ASPECTS." In Recent Advances in Applied Science & Technology towards Sustainable Environment. NOBLE SCIENCE PRESS, 2024. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-16.

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Because of its computing efficiency, precision, and relative simplicity, the Reduced Differential Transform Method (RDTM) has become a powerful analytical tool for solving many types of partial differential equations (PDEs). Our focus here is on time fractional nonlinear PDEs, a large and important class of mathematical models, and how RDTM may be applied to solve them. Traditional solution methods are challenged by the complicated behaviour of these equations, which emerge in different scientific areas including physics, engineering, and biology. This study lays out a full mathematical scheme for solving time fractional nonlinear PDEs using RDTM. First, we provide an overview of RDTM and how it has been modified to deal with fractional derivatives. Afterwards, we describe in detail the process for applying RDTM to nonlinear PDEs with fractional temporal derivatives, elaborating on important computational details and algorithmic stages. We show numerical examples of the methodology in action, showing that it efficiently and accurately solves various time fractional nonlinear PDE types. In addition, we go over the computational details of using RDTM to solve time fractional nonlinear PDEs. In sum, the paper meticulously lays out the theoretical groundwork and computational details of using RDTM to solve time fractional nonlinear PDEs. The offered methodology provides a useful resource for academics and professionals in quest of effective answers to complicated mathematical models found in many scientific and engineering domains. Keywords: Mathematical Framework, Fractional Derivatives, Analytical Solution, Efficiency
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Hemalatha, S., and S. Margret Anouncia. "A Computational Model for Texture Analysis in Images with Fractional Differential Filter for Texture Detection." In Biometrics. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-0983-7.ch014.

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This paper is dedicated to the modelling of textured images influenced by fractional derivatives for texture detection. As most of the images contain textures, texture analysis becomes the most important for image understanding and it is a key solution for many computer vision applications. Hence, texture must be suitably detected and represented. Nevertheless, existing texture detection algorithms consider texture as a unique feature from edges. The proposed model explores a novel way of developing texture detection algorithm by mimicking edge detection algorithms. The method assumes that texture feature is analogous to edges and thus, the time complexity is reduced significantly. The model proposed in this work is based on Gaussian kernel smoothing, Fractional partial derivatives and a statistical approach. It is justified to be robust to noisy images and possesses statistical interpretation. The model is validated by the classification experiments on different types of textured images from Brodatz album. It achieves higher classification accuracy than the existing methods.
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Conference papers on the topic "Fractional partial derivatives"

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Raba, Bana Ali, and Fadime Dal. "Homotopy Perturbation Method Applied to Fractional-order Nonlinear Partial Differential Equations." In 8th International Students Science Congress. ULUSLARARASI ÖĞRENCİ DERNEKLERİ FEDERASYONU (UDEF), 2024. https://doi.org/10.52460/issc.2024.034.

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In this paper, we propose a numerical method for solving nonlinear fractional partial differential equations with fractional time derivatives. The fractional derivative is described in the Caputo sense. This method is based on the homotopy perturbation method. The approximate solutions obtained by our proposed method are in excellent agreement with the exact solutions. It is worthwhile to note that our method is applicable to a variety of fractional partial differential equations occurring in fluid mechanics, signal processing, system identification, control, and robotics.
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Podlubny, Igor, Tomas Skovranek, and Blas M. Vinagre Jara. "Matrix Approach to Discretization of Ordinary and Partial Differential Equations of Arbitrary Real Order: The Matlab Toolbox." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86944.

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The method developed recently by Podlubny et al. (I. Podlubny, Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, pp. 359–386; I. Podlubny et al., Journal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137–3153) makes it possible to immediately obtain the discretization of ordinary and partial differential equations by replacing the derivatives with their discrete analogs in the form of triangular strip matrices. This article presents a Matlab toolbox that implements the matrix approach and allows easy and convenient discretization of ordinary and partial differential equations of arbitrary real order. The basic use of the functions implementing the matrix approach to discretization of derivatives of arbitrary real order (so-called fractional derivatives, or fractional-order derivatives), and to solution of ordinary and partial fractional differential equations, is illustrated by examples with explanations.
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Tangpong, X. W., and Om P. Agrawal. "Fractional Optimal Control of Distributed Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43046.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a Fractional Optimal Control Problem (FOCP) is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). The scheme presented rely on reducing the equations for distributed system into a set of equations that have no space parameter. Several strategies are pointed out for this task, and one of them is discussed in detail. This involves discretizing the space domain into several segments, and writing the spatial derivatives in terms of variables at space node points. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the problem. The numerical technique presented in [1] for scalar case is extended for the vector case. In this technique, the FOC equations are reduced to Volterra type integral equations. The time domain is also descretized into several segments. For the linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for various order of fractional derivatives and various order of space and time discretizations. Numerical results show that for the problem considered, only a few space grid points are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other distributed systems.
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Talib, Imran, Fethi Bin Muhammad Belgacem, Naseer Ahmad Asif, and Hammad Khalil. "On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972616.

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Liu, F., Q. Yang, and I. Turner. "Stability and Convergence of Two New Implicit Numerical Methods for the Fractional Cable Equation." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86578.

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The cable equation is one the most fundamental equations for modeling neuronal dynamics. Cable equations with fractional order temporal operators have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper we consider the following fractional cable equation involving two fractional temporal derivatives: ∂u(x,t)∂t=0Dt1−γ1κ∂2u(x,t)∂x2−μ02Dt1−γ2u(x,t)+f(x,t), where 0 &amp;lt; γ1,γ2 &amp;lt; 1, κ &amp;gt; 0, and μ02 are constants, and 0Dt1−γu(x,t) is the Rieman-Liouville fractional partial derivative of order 1 − γ. Two new implicit numerical methods with convergence order O(τ + h2) and O(τ2 + h2) for the fractional cable equation are proposed respectively, where τ and h are the time and space step sizes. The stability and convergence of these methods are investigated using the energy method. Finally, numerical results are given to demonstrate the effectiveness of both implicit numerical methods. These techniques can also be applied to solve other types of anomalous subdiffusion problems.
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Hao, Bing, and Huan Luo. "Research On the Solution of One Class of Fractional-Order NeuralNetworks with Time Delays and Partial Derivatives." In ADMIT 2023: 2023 2nd International Conference on Algorithms, Data Mining, and Information Technology. ACM, 2023. http://dx.doi.org/10.1145/3625403.3625449.

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Connolly, Thomas J. M., and Jaime A. Contreras. "New Bond Graph Primitive Elements for Modeling Systems Modeled by Practical Derivatives." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14942.

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This paper describes our work in creating and using new bond graph primitive elements to represent time-varying and/or frequency-dependent effects in engineering systems. These phenomena can be mathematically represented by fractional-order differential and integral operators. Equations with such operators arise from the analysis and application of several classes of partial differential equations [1]. Previous researchers (Bagley, Torvik, et. al.) have used this approach to further the modeling of fluid-structure interactions, heat transfer, and related control systems [3–6]. These new primitive elements represent visco-inertial and visco-elastic phenomena, whose constitutive laws are dictated by half-order derivatives and integrals. After a brief overview of the fractional derivative, we continue with a formalized mathematical development of these new primitive elements using an impedance-based approach, which provides further support in the argument for their necessity. This approach provides the system modeler with new tools to widen the range of systems that he can accurately model using a lumped-parameter bond graph approach. We illustrate the application and utility of the approach with an example problem in fluid-structure interactions by presenting bond graph models and corresponding simulations. The simulations reveal that the use of these new elements accurately captures the frequency-dependent behavior of the physical system.
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Dzuliana, F. J., Uddin Salah, Roslan Rozaini, and Md Akhir Mohd Kamalrulzaman. "Modeling electro-magneto-hydrodynamic of blood flow in multi-stenosed artery using fractional deivatives without singular kernel." In FIT-M 2020. Знание-М, 2020. http://dx.doi.org/10.38006/907345-75-1.2020.310.318.

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Stenosis is one of the most common problems in blood flow through arteries. Stenosis means narrowing arteries. Among the various cardiovascular diseases, stenosis is a major one that affects blood flow in the arteries and becomes the leading cause of death worldwide. Therefore, several studies were conducted either experimentally or mathematically to understand stenosis effects on blood flow through arteries. This study investigates the Newtonian fluid’s electro-magneto-hydrodynamic flow mixed with uniformly distributed magnetic particles through a multi-stenosed artery. The fluid is acted by an arbitrary timedependent pressure gradient, external electric and magnetic fields, and the porous medium. The governing equations are considered as fractional partial differential equations based on the Caputo–Fabrizio time-fractional derivatives without singular kernel. The fractional model of blood flow in the multi-stenosed artery will be presented subject to several external factors. These include the severity of the stenosis and the magnetic particles with the presence of an electromagnetic field. The steady and unsteady parts of the pressure gradient that give rise to the systolic and diastolic pressures are considered as the pumping action of the heart, which in turn produces a pressure gradient throughout the human circulatory system. The fractionaloperator’s effect and pertinent system parameters on blood flow axial velocities are presented and discussed for future works.
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Thorat, S. N., K. P. Ghadle, R. A. Muneshwar та K. L. Bondar. "Some properties on modified α-fractional partial derivative with its applications". У 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS (e-ICMTA-2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0164634.

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Fu, Zhuo-Jia. "Radial Basis Function Methods for Fractional Derivative Applications." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-48016.

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In recent decades, the theoretical researches and experimental results show that fractional derivative model can be a powerful tool to describe the contaminant transport through complex porous media and the dynamic behaviors of real viscoelastic materials. Consequently, growing attention has been attracted to numerical solution of fractional derivative model. Radial basis function (RBF) meshless technique is one of the most popular and powerful numerical methods, which are mathematically simple, and avoid troublesome mesh generation for high-dimensional problems involving irregular or moving boundary. Recently, RBF-based meshless methods, such as the Boundary Particle Method and the Method of Approximate Particular Solutions, have been successfully applied to fractional derivative problems. The Boundary Particle Method is one of truly boundary-only RBF collocation schemes, which employs both the semi-analytical basis functions to approximate the FDE solutions. Inspired by the boundary collocation RBF techniques, the Method of Approximate Particular Solutions is one of the domain-type RBF collocation schemes with easy-to-use merit, which employs the particular solution RBFs for the solution of FDEs. This study will make a numerical investigation on the abovementioned RBF meshless methods to fractional derivative problems. The convergence rate, numerical accuracy and stability of these schemes will be examined through several benchmark examples.
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Reports on the topic "Fractional partial derivatives"

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Charusiri, Punya, Wasant Pongsapich, and Chakkaphan Sutthirat. Petrochemistry of probable gem-bearing basalts in Sop Prap-Ko Kha Area, Changwat Lampang : research report. Chulalongkorn University, 1996. https://doi.org/10.58837/chula.res.1996.17.

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The project area covers approximately 300 km[superscript 2] encompassing parts of Amphoe Sop Prap, Amphoe Ko Kha, and Amphoe Mae Tha of Changwat Lampang. The area is mainly occupied by sedimentary (and metamorphic) rocks of Permian, Triassic, Tertiary and Quaternary ages. The Triassic rocks include the Phra That, the Pha Kan, and the Hong Hoi Formations of the Lampang Group. Igneous rocks comprise Permo-Triassic volcanics, Triassic granodiorite, and Cenozoic basalts. Sapphires are frequently found in alluvial and residual deposits, particularly in the northern basaltic area. Sapphires in the south terrain are also encountered in stream channels flowing from nearby Cenozoic basaltic crater. Sapphires are normally blue, dark blue, greenish blue, and dark brown, and occur as angular to subangular forms, ranging size from 0.5 to 6 cm. Basalts in the project area can be geographically subdivided into 2 terrains the north and the south. The northern terrain (Nam Cho Basalt) covers approximately 3 km[superscript 2] in Thambon Nam Cho, Amphoe Mae Tha. The basalts occur as one major flow layer, that flowed following the hill slope. The rocks are characterized by reddish brown vesicular rocks (top), and black dense rocks (bottom). They are generally present as fine-grained and porphyritic. Ultramafic nodules of lherzolite comprising olivine, pyroxene and spinel and megacrysts of olivine, and pyroxene, are often observed in this terrain. Microscopically, the northern basalts invariability occur as microporphyritic to porphyritic, aphanitic. Phenocrysts of olivine and pyroxene are generally surrounded by small plagioclase- microlite groundmass and glass. The basalts are typically composed of plagioclase, pyroxene, olivine, opaque minerals, and other accessories. Average grain size is relatively smaller than that of the south basalts. The southern terrain (Sop Prap-Ko Kha Basalt) can be subdivided into 5 flow layers. Good exposures are typically present at road cut quarries between kms 586-569 on the highway number 1, nearby the volcanic crater. The area covers approximately 55 km[superscript 2] between Amphoe Ko Kha and Amphoe Sop Prap. These five basaltic flows are similarly characterized by vesicular, or massive, microporphyritic-porphyritic, fine-grained to aphanitic rocks. Phenocrysts of oviline frequently occur in most flows. These basalt flows microscopically comprise similar characteristics, mostly they always contain plagioclase, pyroxene, olivine, opaque minerals, and other accessories. Intersertal, and subophitic textures are frequently present in these basalts. Ultramafic nodules are rarely found in this basaltic terrain. Geochemically, that Nam Cho and Sop Prap-Ko Kha Basalts can be clearly divided by difference in major and trace- element contents. Though several variation diagrams display similar trend. The Nam Cho basalts are mainly classified as basanite, where as the Sop Prap-Ko Kha basalts are dominantly alkaline-olivene basalt base on normative plagioclase and hyperstene and/or nepheline. Rare-earth element concentrations show similar chondrite-normalized patterns for most basalt groups. Calculated Mg-values indicate crystal fractionation process of the derivative magmas. [superscript40] Ar/[superscript 39] Ar geochronological data are clearly concluded that Sop Prap-Ko Kha Basalts, ranging in age from younger than 2.30 to 2.41 Ma, are older than Nam Cho Basalts (ca. 2.02 Ma). Therefore, it is tentatively inferred that basalts from both terrains were probably originated from derivative magmas, which are evolved by similar processes, as crustal fraction with subsequent crustal contamination process. However, these derivate magmas may have been derived from different originated sources and primary magmas with low degree of partial melting in mantle. The occurrence of sapphires possibly indicates partial melting of primary magma at high depth and pressure, and crustal fractionations of derivative magma route to 8-10 kbar. Then Nam Cho Basalt can be regarded as gem-related and formed different derivative magma from mantle source region.
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