Relevant bibliographies by topics / Fractional derivative operators

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

Academic literature on the topic 'Fractional derivative operators'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Fractional derivative operators"

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TARASOV, VASILY E. "FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE." International Journal of Mathematics 18, no. 03 (2007): 281–99. http://dx.doi.org/10.1142/s0129167x07004102.

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Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
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Bouzeffour, Fethi. "Advancing Fractional Riesz Derivatives through Dunkl Operators." Mathematics 11, no. 19 (2023): 4073. http://dx.doi.org/10.3390/math11194073.

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The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context of Dunkl-type operators. A particularly noteworthy revelation is that when a specific parameter κ equals zero, the Riesz–Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.
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Pskhu, Arsen. "Nakhushev extremum principle for a class of integro-differential operators." Fractional Calculus and Applied Analysis 23, no. 6 (2020): 1712–22. http://dx.doi.org/10.1515/fca-2020-0085.

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Abstract We investigate extreme properties of a class of integro-differential operators. We prove an assertion that extends the Nakhushev extremum principle, known for fractional Riemann-Liouville derivatives, to integro-differential operators with kernels of a general form. We establish the weighted extremum principle for convolution operators and the Riemann-Liouville fractional derivative. In addition, as an application, we prove a uniqueness theorem for a boundary value problem in a non-cylindrical domain for the fractional diffusion equation with the Riemann-Lioville fractional derivative
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Inbaig, Abdlgader M., and Yasmina M. Bashon. "A comparative study on the behavior of Riemann-Liouville and Caputo fractional derivatives of some functions." Libyan Journal of Science &Technology 14, no. 2 (2025): 127–38. https://doi.org/10.37376/ljst.v14i2.7209.

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This paper presents an overview of fractional order derivative operators. Particular attention is devoted to the Riemann-Liouville and Caputo fractional derivative operators. A comparative study of these two frameworks to show how they behave geometrically. The computation results of some elementary function derivatives of fractional order are shown in graphic form and tabular for this purpose. The conclusion will include a few observations about derivatives of integer and fr Abdlgader M. Inbaig, Yasmina M. Bashon actional order.
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Mortari, Daniele, Roberto Garrappa, and Luigi Nicolò. "Theory of Functional Connections Extended to Fractional Operators." Mathematics 11, no. 7 (2023): 1721. http://dx.doi.org/10.3390/math11071721.

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The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context of fractional-order operators (integrals and derivatives). The extension was performed and presented for univariate functions, with the aim of determining the whole set of functions satisfying some constraints expressed in terms of integrals and derivatives of non-integer order. The objective of these expressions was to solve fractional differential equations or other problems subject to fractional constraints. Although this work focused on the Riemann–Liouville def
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Martínez-Fuentes, Oscar, Fidel Meléndez-Vázquez, Guillermo Fernández-Anaya, and José Francisco Gómez-Aguilar. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities." Mathematics 9, no. 17 (2021): 2084. http://dx.doi.org/10.3390/math9172084.

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In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators and, in particular, the main existing fractional derivatives. Based on the conditions for the Laplace transform of these operators, in this paper, some new results are obtained—for example, relationships between Riemann–Liouville and Caputo derivatives and inverse operators. Later, employing a representation for the product of two functions, we
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Tarasov, Vasily E. "Fractional Derivative Regularization in QFT." Advances in High Energy Physics 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/7612490.

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We propose in this paper a new regularization, where integer-order differential operators are replaced by fractional-order operators. Regularization for quantum field theories based on application of the Riesz fractional derivatives of noninteger orders is suggested. The regularized loop integrals depend on parameter that is the order α>0 of the fractional derivative. The regularization procedure is demonstrated for scalar massless fields in φ4-theory on n-dimensional pseudo-Euclidean space-time.
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Garrappa, Roberto, Eva Kaslik, and Marina Popolizio. "Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial." Mathematics 7, no. 5 (2019): 407. http://dx.doi.org/10.3390/math7050407.

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Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly used operators and illustrated two approaches to generalize integer-order derivatives to fractional order; the aim was to provide a tool for a full understanding of the specific features of each fractional derivative and to better highlight their differences. We hence provided a guide to the evaluation of fractional integrals and derivatives of so
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Azzouz, Noureddine, Bouharket Benaissa та Hüseyin Budak. "Ongeneralized ψ-conformable calculus: Properties and inequalities". Filomat 38, № 25 (2024): 8755–72. https://doi.org/10.2298/fil2425755a.

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In this paper, we first introduce a new fractional derivatives and integrals called generalized ?-conformable derivative and generalized ?-conformable integral operators, respectively. We also show that these operators generalize various well-known fractional integral operators. Then, we present several properties of these operators including semi-group property. Moreover, we apply these operators to obtain a new Hermite-Hadamard-type inequality for convex functions. Furthermore, we obtain corresponding midpoint and trapezoid type inequalities for functions whose derivatives in absolute value
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Odibat, Zaid, and Dumitru Baleanu. "On a New Modification of the Erdélyi–Kober Fractional Derivative." Fractal and Fractional 5, no. 3 (2021): 121. http://dx.doi.org/10.3390/fractalfract5030121.

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In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdélyi–Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputo-type Erdélyi–Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.
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Dissertations / Theses on the topic "Fractional derivative operators"

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Bologna, Mauro. "The Dynamic Foundation of Fractal Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4235/.

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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and
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BUCUR, CLAUDIA DALIA. "Some nonlocal operators and effects due to nonlocality." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/10281/277792.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive introduction to the fractional Laplacian, we present some related contemporary research results and we add some original material. Indeed, we study the potential theory of this operator, introduce a new proof of Schauder estimates using the potential theory approach, we study a fractional elliptic problem in Rn with convex nonlinearities and critical growth and we presen
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Bucur, C. D. "SOME NONLOCAL OPERATORS AND EFFECTS DUE TO NONLOCALITY." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/488032.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and some other types of fractional derivatives. We make an extensive introduction to the fractional Laplacian and to some related contemporary research themes. We add to this some original material: the potential theory of this operator and a proof of Schauder estimates with the potential theory approach, the study of a fractional elliptic problem in $mathbb{R}^n$ with convex nonlinearities and critical growth, and a stickiness property of $s$-minimal surfaces as $s$ gets small. Also,
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Amsheri, Somia Muftah Ahmed. "Fractional calculus operator and its applications to certain classes of analytic functions : a study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and ρ-valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of ρ-valent functions with negative coefficients in the open unit disk such as classes of ρ-valent starlike f
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Amsheri, Somia M. A. "Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of -valent functions with negative coefficients in the open unit disk such as classes of -valent starlike func
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Jiang, Xin. "A Systematic Approach for Digital Hardware Realization of Fractional-Order Operators and Systems." University of Akron / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1386649994.

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Miloš, Japundžić. "Uopštena rešenja nekih klasa frakcionih parcijalnih diferencijalnih jednačina." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2016. https://www.cris.uns.ac.rs/record.jsf?recordId=102114&source=NDLTD&language=en.

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Doktorska disertacija je posvećena rešavanju Košijevog problema odabranih klasa frakcionih diferencijalnih jednačina u okviru Kolomboovih prostora uopštenih funkcija. U prvom delu disertacije razmatrane su nehomogene evolucione jednačine sa prostorno frakcionim diferencijalnim operatorima reda 0 < α < 2 i koeficijentima koji zavise od x i t. Ova klasa jednačina je aproksimativno rešavana, tako što je umesto početne jednačine razmatrana aproksimativna jednačina data preko regularizovanih frakcionih izvoda, odnosno, njihovih regularizovanih množitel
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Monyayi, Victor Tebogo. "Well-posedness and mathematical analysis of linear evolution equations with a new parameter." Diss., 2020. http://hdl.handle.net/10500/26794.

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Abstract in English<br>In this dissertation we apply linear evolution equations to the Newtonian derivative, Caputo time fractional derivative and $-time fractional derivative. It is notable that the most utilized fractional order derivatives for modelling true life challenges are Riemann- Liouville and Caputo fractional derivatives, however these fractional derivatives have the same weakness of not satisfying the chain rule, which is one of the most important elements of the match asymptotic method [2, 3, 16]. Furthermore the classical bounded perturbation theorem associated with Rieman
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Toudjeu, Ignace Tchangou. "Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative." Diss., 2019. http://hdl.handle.net/10500/25774.

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Linear Evolution Equations (LEE) have been studied extensively over many years. Their extension in the field of fractional calculus have been defined by Dαu(x, t) = Au(x, t), where α is the fractional order and Dα is a generalized differential operator. Two types of generalized differential operators were applied to the LEE in the state-of-the-art, producing the Riemann-Liouville and the Caputo time fractional evolution equations. However the extension of the new Caputo-Fabrizio derivative (CFFD) to these equations has not been developed. This work investigates existing fractional derivative
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Singh, Satwinder Jit. "New Solution Methods For Fractional Order Systems." Thesis, 2007. https://etd.iisc.ac.in/handle/2005/885.

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This thesis deals with developing Galerkin based solution strategies for several important classes of differential equations involving derivatives and integrals of various fractional orders. Fractional order calculus finds use in several areas of science and engineering. The use of fractional derivatives may arise purely from the mathematical viewpoint, as in controller design, or it may arise from the underlying physics of the material, as in the damping behavior of viscoelastic materials. The physical origins of the fractional damping motivated us to study viscoelastic behavior of disordered
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Books on the topic "Fractional derivative operators"

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Fractional-Order Integral and Derivative Operators and Their Applications. MDPI, 2020. http://dx.doi.org/10.3390/books978-3-03936-651-4.

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Fractional-Order Integral and Derivative Operators and Their Applications. Mdpi AG, 2020.

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Namsrai, Kh. New Approach to Analytic Calculation: Derivation of Universal Formulas for Calculation of Definite Integrals, Fractional Derivatives and Inverse Operators by Hand. Lulu Press, Inc., 2014.

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Book chapters on the topic "Fractional derivative operators"

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Sene, Ndolane. "Analytical Solutions for the Fluid Model Described by Fractional Derivative Operators Using Special Functions in Fractional Calculus." In Special Functions in Fractional Calculus and Engineering. CRC Press, 2023. http://dx.doi.org/10.1201/9781003368069-2.

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Kadam, Pratik, Gaurav Datkhile, and Vishwesh A. Vyawahare. "Artificial Neural Network Approximation of Fractional-Order Derivative Operators: Analysis and DSP Implementation." In Trends in Mathematics. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9227-6_6.

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Dzieliński, Andrzej, Dominik Sierociuk, Wiktor Malesza, Michał Macias, Michał Wiraszka, and Piotr Sakrajda. "Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling." In Studies in Systems, Decision and Control. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-89972-1_4.

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Bansal, Manish Kumar, Devendra Kumar, and Junesang Choi. "Certain Image Formulae of the Incomplete I-Function Under the Conformable and Pathway Fractional Integral and Derivative Operators." In Advances in Mathematical Modelling, Applied Analysis and Computation. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0179-9_7.

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Kıymaz, İ. O., P. Agarwal, S. Jain, and A. Çetinkaya. "On a New Extension of Caputo Fractional Derivative Operator." In Trends in Mathematics. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4337-6_11.

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Shikongo, Albert, Samuel M. Nuugulu, David Elago, Andreas T. Salom, and Kolade M. Owolabi. "Fractional Derivative Operator on Quarantine and Isolation Principle for COVID-19." In Advanced Numerical Methods for Differential Equations. CRC Press, 2021. http://dx.doi.org/10.1201/9781003097938-9.

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Kiryakova, Virginia, and Yuri Luchko. "Multiple Erdélyi–Kober integrals and derivatives as operators of generalized fractional calculus." In Basic Theory, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571622-006.

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Husain, Saddam, and Nabiullah Khan. "Certain Generalization of Appell’s Functions and Riemann–Liouville Fractional Derivative Operator and Their Applications." In Forum for Interdisciplinary Mathematics. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-8715-9_10.

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Leventides, John, Evangelos Melas, Costas Poulios, and Paraskevi Boufounou. "Koopman Operators and Extended Dynamic Mode Decomposition for Economic Growth Models in Terms of Fractional Derivatives." In Lecture Notes in Operations Research. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-29050-3_3.

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Agarwal, Ritu, and J. Sokol. "On $$\alpha $$ α -Convex Multivalent Functions Defined by Generalized Ruscheweyh Derivatives Involving Fractional Differential Operator." In Advances in Intelligent Systems and Computing. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-1602-5_22.

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Conference papers on the topic "Fractional derivative operators"

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Sokolovskyy, Yaroslav, Denys Manokhin, and Olha Mokrytska. "Segmentation of Medical Images Using Deep Learning and Texture Enhancement Based on Fractional Derivative Operators." In 2024 IEEE 19th International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH). IEEE, 2024. http://dx.doi.org/10.1109/memstech63437.2024.10620036.

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Lorenzo, Carl F., and Tom T. Hartley. "On Self-Consistent Operators With Application to Operators of Fractional Order." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86730.

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This paper extends the idea of the initialization function to the more general concept of a continuation function. The paper sets forth definitions for operator self-consistency which are then applied to test three operators, the ordinary Riemann integral, the time-varying initialized Riemann-Liouville fractional integral, and finally the Caputo derivative. Self-consistency was found for the first two cases. The Caputo fractional derivative operator was found to be self-inconsistent based on possible continuation functions derived from the Laplace transform of the derivative. A theoretical con
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Lorenzo, Carl F., and Tom T. Hartley. "Initialization of Fractional Differential Equations: Background and Theory." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34810.

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It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order operators. This paper provides background on past work in the area and determines the Laplace transforms for initialized fractional integrals of any order and fractional derivatives of order less than one. A companion paper in this conference extends the theo
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Lorenzo, Carl F., and Tom T. Hartley. "Initialization of Fractional Differential Equations: Theory and Application." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34814.

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It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order operators. A companion paper in this conference determines the Laplace transforms for initialized fractional integrals of any order and fractional derivatives of order less than one. This paper extends the theory for the Laplace transform of the derivative to
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Zhang, Junjian, Guoyi Ke, and Z. Charlie Zheng. "Time-Domain Simulation of Ultrasound Propagation With Fractional Laplacian." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65966.

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The simulation is developed for the purpose of simulating ultrasound propagation through biological tissues. The simulation is based on the time-domain conservation laws with the governing equations for acoustic pressure and velocity, with frequency dependent absorption and dispersion effects. We use forward differencing for velocity and backward differencing for pressure on the non-fractional derivative operator terms in spatial discretization. The fractional Laplacian operators are treated as Riesz derivatives. The shifted standard Grunwald approximation method is used to solve fractional de
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Xu, Yufeng, and Om P. Agrawal. "Numerical Solutions of Generalized Oscillator Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12705.

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Harmonic oscillators play a fundamental role in many areas of science and engineering, such as classical mechanics, electronics, quantum physics, and others. As a result, harmonic oscillators have been studied extensively. Classical harmonic oscillators are defined using integer order derivatives. In recent years, fractional derivatives have been used to model the behaviors of damped systems more accurately. In this paper, we use three operators called K-, A- and B-operators to define the equation of motion of an oscillator. In contrast to fractional integral and derivative operators which use
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Chen, Dali, Dingyu Xue, and YangQuan Chen. "Digital Fractional Order Savitzky-Golay Differentiator and Its Application." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47864.

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Firstly the one-dimension digital fractional order Savitzky-Golay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure robust and accuracy. Experiments demonstrate that 1-D DFOSGD can estimate the fractional order derivatives of both ideal signal and noisy signal accurately. Secondly, the two-dimension DFOSGD is obtained f
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Федоров, Владимир, and Николай Филин. "Analytic resolving families of operators for equations with discretely distributed fractional derivative." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.86.

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Miles, Paul, Graham Pash, William Oates, and Ralph C. Smith. "Numerical Techniques to Model Fractional-Order Nonlinear Viscoelasticity in Soft Elastomers." In ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/smasis2018-8102.

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Dielectric elastomers are employed on a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many instances a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-o
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Catania, Giuseppe, and Silvio Sorrentino. "Experimental Identification of a Fractional Derivative Linear Model for Viscoelastic Materials." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85725.

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Non integer, fractional order derivative rheological models are known to be very effective in describing the linear viscoelastic dynamic behaviour of mechanical structures made of polymers [1]. The application of fractional calculus to viscoelasticity can be physically consistent [2][3][4] and the resulting non integer order differential stress-strain constitutive relation provides good curve fitting properties, requires only a few parameters and leads to causal behaviour [5]. When using such models the solution of direct problems, i.e. the evaluation of time or frequency response from a known
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