Relevant bibliographies by topics / Fractional derivatives

Contents

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

Academic literature on the topic 'Fractional derivatives'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Fractional derivatives.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Fractional derivatives"

1

Feng, Xiaobing, and Mitchell Sutton. "A new theory of fractional differential calculus." Analysis and Applications 19, no. 04 (February 20, 2021): 715–50. http://dx.doi.org/10.1142/s0219530521500019.

Full text
Abstract:
This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize what functions are fractionally differentiable. Various calculus rules including a fundamental theorem calculus, product and chain rules, and integration by parts formulas are established for weak fractional derivatives. Additionally, relationships with classical fractional derivatives and detailed characterizations of weakly fractional differentiable functions are also established. Furthermore, the notion of weak fractional derivatives is also systematically extended to general distributions instead of only to some special distributions. This new theory lays down a solid theoretical foundation for systematically and rigorously developing new theories of fractional Sobolev spaces, fractional calculus of variations, and fractional PDEs as well as their numerical solutions in subsequent works.
APA, Harvard, Vancouver, ISO, and other styles
2

Ortigueira, Manuel Duarte, and Gabriel Bengochea. "Bilateral Tempered Fractional Derivatives." Symmetry 13, no. 5 (May 8, 2021): 823. http://dx.doi.org/10.3390/sym13050823.

Full text
Abstract:
The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and shows that it cannot be considered as a derivative.
APA, Harvard, Vancouver, ISO, and other styles
3

Farayola, Musiliu Folarin, Sharidan Shafie, Fuaada Mohd Siam, Rozi Mahmud, and Suraju Olusegun Ajadi. "Mathematical modeling of cancer treatments with fractional derivatives: An Overview." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (August 31, 2021): 389–401. http://dx.doi.org/10.11113/mjfas.v17n4.2062.

Full text
Abstract:
This review article presents fractional derivative cancer treatment models to show the importance of fractional derivatives in modeling cancer treatments. Cancer treatment is a significant research area with many mathematical models developed by mathematicians to represent the cancer treatment processes like hyperthermia, immunotherapy, chemotherapy, and radiotherapy. However, many of these models were based on ordinary derivatives and the use of fractional derivatives is still new to many mathematicians. Therefore, it is imperative to review fractional cancer treatment models. The review was done by first presenting 22 various definitions of fractional derivative. Thereafter, 11 articles were selected from different online databases which included Scopus, EBSCOHost, ScienceDirect Journal, SpringerLink Journal, Wiley Online Library, and Google Scholar. These articles were summarized, and the used fractional derivative models were analyzed. Based on this analysis, the merit of modeling with fractional derivative, the most used fractional derivative definition, and the future direction for cancer treatment modeling were presented. From the results of the analysis, it was shown that fractional derivatives incorporated memory effects which gave it an advantage over ordinary derivative for cancer treatment modeling. Moreover, the fractional derivative is a general definition of all derivatives. Also, the fractional models can be applied to different cancer treatment procedures and the most used fractional derivative is the Caputo as well as its non-singular kernel versions. Finally, it was concluded that the future direction for cancer treatment modeling is the adoption of fractional derivative models corroborated with experimental or clinical data.
APA, Harvard, Vancouver, ISO, and other styles
4

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
5

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

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
6

Sene, Ndolane, and José Francisco Gómez Aguilar. "Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives." Fractal and Fractional 3, no. 3 (July 7, 2019): 39. http://dx.doi.org/10.3390/fractalfract3030039.

Full text
Abstract:
This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville–Caputo left generalized fractional derivative and the left generalized fractional derivative were used. The behaviors of the analytical solutions of the mass-spring-damper systems described by the left generalized fractional derivative and the Liouville–Caputo left generalized fractional derivative were represented graphically and the effect of the orders of the fractional derivatives analyzed. We finish by analyzing the global asymptotic stability and the converging-input-converging-state of the unforced mass-damper system, the unforced spring-damper, the spring-damper system, and the mass-damper system.
APA, Harvard, Vancouver, ISO, and other styles
7

Atangana, Abdon, and Aydin Secer. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/279681.

Full text
Abstract:
The purpose of this note is to present the different fractional order derivatives definition that are commonly used in the literature on one hand and to present a table of fractional order derivatives of some functions in Riemann-Liouville sense On other the hand. We present some advantages and disadvantages of these fractional derivatives. And finally we propose alternative fractional derivative definition.
APA, Harvard, Vancouver, ISO, and other styles
8

İlhan, Esin, and İ. Onur Kıymaz. "A generalization of truncated M-fractional derivative and applications to fractional differential equations." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 171–88. http://dx.doi.org/10.2478/amns.2020.1.00016.

Full text
Abstract:
AbstractIn this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.
APA, Harvard, Vancouver, ISO, and other styles
9

Hattaf, Khalid. "On Some Properties of the New Generalized Fractional Derivative with Non-Singular Kernel." Mathematical Problems in Engineering 2021 (May 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/1580396.

Full text
Abstract:
This paper presents some new formulas and properties of the generalized fractional derivative with non-singular kernel that covers various types of fractional derivatives such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. These new properties extend many recent results existing in the literature. Furthermore, the paper proposes some interesting inequalities that estimate the generalized fractional derivatives of some specific functions. These inequalities can be used to construct Lyapunov functions with the aim to study the global asymptotic stability of several fractional-order systems arising from diverse fields of science and engineering.
APA, Harvard, Vancouver, ISO, and other styles
10

Garrappa, Roberto, Eva Kaslik, and Marina Popolizio. "Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial." Mathematics 7, no. 5 (May 7, 2019): 407. http://dx.doi.org/10.3390/math7050407.

Full text
Abstract:
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 some elementary functions and studied the action of different derivatives on the same function. In particular, we observed how Riemann–Liouville and Caputo’s derivatives converge, on long times, to the Grünwald–Letnikov derivative which appears as an ideal generalization of standard integer-order derivatives although not always useful for practical applications.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Fractional derivatives"

1

Katugampola, Don Udita Nalin. "ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/dissertations/387.

Full text
Abstract:
In this paper we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin transforms of such generalized fractional operators which are important in solving fractional differential equations.
APA, Harvard, Vancouver, ISO, and other styles
2

Traytak, Sergey D., and Tatyana V. Traytak. "Method of fractional derivatives in time-dependent diffusion." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193646.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Schiavone, S. E. "Distributional theories for multidimensional fractional integrals and derivatives." Thesis, University of Strathclyde, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382492.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Traytak, Sergey D., and Tatyana V. Traytak. "Method of fractional derivatives in time-dependent diffusion." Diffusion fundamentals 6 (2007) 38, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14215.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Munkhammar, Joakim. "Riemann-Liouville Fractional Derivatives and the Taylor-Riemann Series." Thesis, Uppsala University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121418.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Shi, Chen Yang. "High order compact schemes for fractional differential equations with mixed derivatives." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691348.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Haveroth, Thais Clara da Costa. "On the use of fractional derivatives for modeling nonlinear viscoelasticity." Universidade do Estado de Santa Catarina, 2015. http://tede.udesc.br/handle/handle/2069.

Full text
Abstract:
Made available in DSpace on 2016-12-12T20:25:13Z (GMT). No. of bitstreams: 1 Thais Clara da Costa Haveroth.pdf: 3726370 bytes, checksum: 204349100247f52ea6bf4916ec49a0ab (MD5) Previous issue date: 2015-10-26
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Dentre a vasta gama de polímeros estruturais atualmente disponíveis no mercado, este trabalho está particularmente voltado ao estudo do polietileno de alta densidade. Embora este material já tenha sido investigado por diversos autores, seu típico comportamento viscoelástico não-linear apresenta dificuldades na modelagem. Visando uma nova contribuição, este trabalho propõe a descrição de tal comportamento utilizando uma abordagem baseada em derivadas fracionários. Esta formulação produz equações constitutivas fracionais que resultam em boas propriedades de ajuste de curvas com menos parâmetros a serem identificados que nos métodos tradicionais. Neste sentido, os resultados experimentais de fluência para o polietileno de alta densidade, avaliados em diferentes níveis de tensão, são ajustados por este esquema. Para estimar a deformação à níveis de tensão que não tenham sido medidos experimentalmente, o princípio da equivalência tensão-tempo é utilizado e os resultados são comparados com aqueles apresentados por uma interpolação linear dos parâmetros. Além disso, o princípio da superposição modificado é aplicado para predizer a comportamento de materiais sujeitos a níveis de tensão que mudam abruptamente ao longo do tempo. Embora a abordagem fracionária simplifique o problema de otimização inversa subjacente, é observado um grande aumento no esforço computacional. Assim, alguns algoritmos que objetivam economia computacional, são estudados. Conclui-se que, quando acurária é necessária ou quando um modelo de séries Prony requer um número muito grande de parâmetros, a abordagem fracionária pode ser uma opção interessante.
Among the wide range of structural polymers currently available in the market, this work is concerned particularly with high density polyethylene. The typical nonlinear viscoelastic behavior presented by this material is not trivial to model, and has already been investigated by many authors in the past. Aiming at a further contribution, this work proposes modeling this material behavior using an approach based on fractional derivatives. This formulation produces fractional constitutive equations that result in good curve-fitting properties with less parameters to be identified when compared to traditional methods. In this regard, experimental creep results of high density polyethylene evaluated at different stress levels are fitted by this scheme. To estimate creep at stress levels that have not been measured experimentally, the time-stress equivalence principle is used and the results are compared with those presented by a linear interpolation of the parameters. Furthermore, the modified superposition principle is applied to predict the strain for materials subject to stress levels which change abruptly from time to time. Some comparative results are presented showing that the fractional approach proposed in this work leads to better results in relation to traditional formulations described in the literature. Although the fractional approach simplifies the underlying inverse optimization problem, a major increase in computational effort is observed. Hence, some algorithms that show computational cost reduction, are studied. It is concluded that when high accuracy is mandatory or when a Prony series model requires a very large number of parameters, the fractional approach may be an interesting option.
APA, Harvard, Vancouver, ISO, and other styles
8

Atkins, Zoe. "Almost sharp fronts : limit equations for a two-dimensional model with fractional derivatives." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55759/.

Full text
Abstract:
We consider the evolution of sharp fronts and almost-sharp fronts for the ↵-equation, where for an active scalar q the corresponding velocity is defined by u = r?(−#)−(2 − ↵)/2q for 0 < ↵ < 1. This system is introduced as a model interpolating between the two-dimensional Euler equation (↵ = 0) and the surface quasi-geostrophic (SQG) equation (↵ = 1). The study of such fronts for the SQG equation was introduced as a natural extension when searching for potential singularities for the three-dimensional Euler equation due to similarities between these two systems, with sharp-fronts corresponding to vortex-lines in the Euler case (Constantin et al., 1994b). Almost-sharp fronts were introduced in C´ordoba et al. (2004) as a regularisation of a sharp front with thickness $, with interest in the study of such solutions as $ ! 0, in particular those that maintain their structure up to a time independent of $. The construction of almost-sharp front solutions to the SQG equation is the subject of current work (Fe↵erman and Rodrigo, 2012). The existence of exact solutions remains an open problem. For the ↵-equation we prove analogues of several known theorems for the SQG equations and extend these to investigate the construction of almost-sharp front solutions. Using a version of the Abstract Cauchy Kovalevskaya theorem (Safonov, 1995) we show for fixed 0 < ↵ < 1, under analytic assumptions, the existence and uniqueness of approximate solutions and exact solutions for short-time independent of $; such solutions take a form asymptotic to almost-sharp fronts. Finally, we obtain the existence and uniqueness of analytic almost-sharp front solutions.
APA, Harvard, Vancouver, ISO, and other styles
9

Blanc, Emilie. "Time-domain numerical modeling of poroelastic waves : the Biot-JKD model with fractional derivatives." Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00954506.

Full text
Abstract:
Une modélisation numérique des ondes poroélastiques, décrites par le modèle de Biot, est proposée dans le domaine temporel. La dissipation visqueuse à l'intérieur des pores est décrite par le modèle de perméabilité dynamique, développé par Johnson-Koplik-Dashen (JKD). Certains coefficients du modèle de Biot-JKD sont proportionnels à la racine carrée de la fréquence : dans le domaine temporel, ces coefficients introduisent des dérivées fractionnaires décalées d'ordre 1/2, qui reviennent à un produit de convolution. Basé sur une représentation diffusive, le produit de convolution est remplacé par un nombre fini de variables de mémoire, dont la relaxation est gouvernée par une équation différentielle ordinaire locale en temps, ce qui mène au modèle de Biot-DA (approximation diffusive). Les propriétés du modèle de Biot-JKD et du modèle de Biot-DA sont analysées : hyperbolicité, décroissance de l'énergie, dispersion. Pour déterminer les coefficients de l'approximation diffusive, différentes méthodes de quadrature sont proposées : quadratures de Gauss, procédures d'optimisation linéaire ou non-linéaire sur la plage de fréquence d'intérêt. On montre que l'optimisation non-linéaire est la meilleure méthode de détermination. Le système est modélisé numériquement en utilisant une méthode de splitting : la partie propagative est discrétisée par un schéma aux différences finies ADER, d'ordre 4 en espace et en temps, et la partie diffusive est intégrée exactement. Une méthode d'interface immergée est implémentée pour discrétiser la géometrie sur une grille cartésienne et pour discrétiser les conditions de saut aux interfaces. Des simulations numériques sont présentées, pour des milieux isotropes et isotropes transverses. Des comparaisons avec des solutions analytiques montrent l'efficacité et la précision de cette approche. Des simulations numériques en milieux complexes sont réalisées : influence de la porosité d'os spongieux, diffusion multiple en milieu aléatoire.
APA, Harvard, Vancouver, ISO, and other styles
10

Fernandez, Arran. "Analysis in fractional calculus and asymptotics related to zeta functions." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/284390.

Full text
Abstract:
This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems and processes, but a full development of the mathematical theory remains incomplete. Many techniques for partial differential equations (PDEs) can be extended to fractional PDEs too. Three chapters below cover my results in this area: establishing the elliptic regularity theorem, Malgrange-Ehrenpreis theorem, and unified transform method for fractional PDEs. Each one is analogous to a known result for classical PDEs, but the proof in the general fractional scenario requires new ideas and modifications. Fractional derivatives and integrals are not uniquely defined: there are many different formulae, each of which has its own advantages and disadvantages. The most commonly used is the classical Riemann-Liouville model, but others may be preferred in different situations, and now new fractional models are being proposed and developed each year. This creates many opportunities for new research, since each time a model is proposed, its mathematical fundamentals need to be examined and developed. Two chapters below investigate some of these new models. My results on the Atangana-Baleanu model proposed in 2016 have already had a noticeable impact on research in this area. Furthermore, this model and the results concerning it can be extended to more general fractional models which also have certain desirable properties of their own. Fractional calculus and zeta functions have rarely been united in research, but one chapter below covers a new formula expressing the Lerch zeta function as a fractional derivative of an elementary function. This result could have many ramifications in both fields, which are yet to be explored fully. Zeta functions are very important in analytic number theory: the Riemann zeta function relates to the distribution of the primes, and this field contains some of the most persistent open problems in mathematics. Since 2012, novel asymptotic techniques have been applied to derive new results on the growth of the Riemann zeta function. One chapter below modifies some of these techniques to prove asymptotics to all orders for the Hurwitz zeta function. Many new ideas are required, but the end result is more elegant than the original one for Riemann zeta, because some of the new methodologies enable different parts of the argument to be presented in a more unified way. Several related problems involve asymptotics arbitrarily near a stationary point. Ideally it should be possible to find uniform asymptotics which provide a smooth transition between the integration by parts and stationary phase methods. One chapter below solves this problem for a particular integral which arises in the analysis of zeta functions.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Fractional derivatives"

1

Gómez, José Francisco, Lizeth Torres, and Ricardo Fabricio Escobar, eds. Fractional Derivatives with Mittag-Leffler Kernel. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11662-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Uchaikin, Vladimir V. Fractional Derivatives for Physicists and Engineers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33911-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

A, Kilbas A., and Marichev O. I, eds. Fractional integrals and derivatives: Theory and applications. Switzerland: Gordon and Breach Science Publishers, 1993.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Brychkov, I︠U︡ A. Handbook of special functions: Derivatives, integrals, series, and other formulas. Boca Raton: CRC Press, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Brychkov, I︠U︡ A. Handbook of special functions: Derivatives, integrals, series and other formulas. Boca Raton: CRC Press, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Gao, Feng, Xiao-Jun Yang, and Ju Yang. General Fractional Derivatives with Applications in Viscoelasticity. Elsevier Science & Technology Books, 2020.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Gao, Feng, Xiao-Jun Yang, and Ju Yang. General Fractional Derivatives with Applications in Viscoelasticity. Elsevier Science & Technology, 2020.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

General Fractional Derivatives with Applications in Viscoelasticity. Elsevier, 2020. http://dx.doi.org/10.1016/c2018-0-01749-1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Uchaikin, Vladimir V. Fractional Derivatives for Physicists and Engineers: Background and Theory. 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Fractional Differential Equations - An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications. Elsevier, 1999. http://dx.doi.org/10.1016/s0076-5392(99)x8001-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Fractional derivatives"

1

Capelas de Oliveira, Edmundo. "Fractional Derivatives." In Studies in Systems, Decision and Control, 169–222. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20524-9_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Zhao, Xuan, and Zhi-Zhong Sun. "Time-fractional derivatives." In Numerical Methods, edited by George Em Karniadakis, 23–48. Berlin, Boston: De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571684-002.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Yang, Xiao-Jun. "Introduction." In General Fractional Derivatives, 1–37. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429284083-1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Yang, Xiao-Jun. "Fractional Derivatives of Constant Order and Applications." In General Fractional Derivatives, 39–142. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429284083-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Yang, Xiao-Jun. "General Fractional Derivatives of Constant Order and Applications." In General Fractional Derivatives, 145–234. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429284083-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Yang, Xiao-Jun. "Fractional Derivatives of Variable Order and Applications." In General Fractional Derivatives, 235–66. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429284083-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Yang, Xiao-Jun. "Fractional Derivatives of Variable Order with Respect to Another Function and Applications." In General Fractional Derivatives, 267–88. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429284083-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Uchaikin, Vladimir V. "Fractional Differentiation." In Fractional Derivatives for Physicists and Engineers, 199–255. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33911-0_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Ortigueira, Manuel Duarte. "The Causal Fractional Derivatives." In Fractional Calculus for Scientists and Engineers, 5–41. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0747-4_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Ortigueira, Manuel Duarte. "Two-Sided Fractional Derivatives." In Fractional Calculus for Scientists and Engineers, 101–21. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0747-4_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Fractional derivatives"

1

Kuroda, Masaharu. "Fractional Derivatives and Complex Modes of Vibration." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86933.

Full text
Abstract:
As described herein, we develop a method to obtain a fractional derivative response of a vibratory system with multiple degrees of freedom (DOF). To obtain fractional-order derivatives/integrals of dynamic response at a certain point on a structure presents technical difficulties because measurements of fractional-order derivative/integral responses in structural dynamics yield some implementation techniques. However, our method obviates special sensors with additional signal-conversion functions. Therefore, existing displacement and velocity sensors can work. Obtaining fractional derivative responses can be accomplished using three methods. Using any of the three methods, fractional states can be expressed with complex vibration modes, in which each point of the system oscillates with a phase that is different from “in-phase” or “out-of-phase.”
APA, Harvard, Vancouver, ISO, and other styles
2

Pooseh, Shakoor, Helena Sofia Rodrigues, Delfim F. M. Torres, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Fractional Derivatives in Dengue Epidemics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636838.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Baleanu, Dumitru, Om P. Agrawal, and Sami I. Muslih. "Lagrangians With Linear Velocities Within Hilfer Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47953.

Full text
Abstract:
Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.
APA, Harvard, Vancouver, ISO, and other styles
4

Sousa, Ercilia. "A close look at fractional derivatives approximations." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967384.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Ortigueira, Manuel D., and Juan J. Trujillo. "On a Unified Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47317.

Full text
Abstract:
A new fractional derivative of complex Gru¨wald-Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Gru¨wald-Letnikov and other fractional derivatives well known. Several properties of such generalized operator are presented.
APA, Harvard, Vancouver, ISO, and other styles
6

Ortigueira, Manuel Duarte, and Arnaldo Guimara˜es Batista. "A New Look at the Fractional Brownian Motion Definition." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35218.

Full text
Abstract:
A reinterpretation of the classic definition of fractional Brownian motion leads to a new definition involving a fractional noise obtained as a fractional derivative of white noise. To obtain this fractional noise, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. For these derivatives the autocorrelation functions of the corresponding fractional noises have the same representations. The obtained results are used to define and propose a new simulation procedure.
APA, Harvard, Vancouver, ISO, and other styles
7

Unser, Michael A., and Thierry Blu. "Fractional wavelets, derivatives, and Besov spaces." In Optical Science and Technology, SPIE's 48th Annual Meeting, edited by Michael A. Unser, Akram Aldroubi, and Andrew F. Laine. SPIE, 2003. http://dx.doi.org/10.1117/12.507443.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Shastri, Subramanian V., and Kumpati S. Narendra. "Fractional Order Derivatives in Systems Theory." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147605.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Jimenez-Garcia, Jesus, and G. Rodriguez-Zurita. "Phase object tomography with fractional derivatives." In IV Iberoamerican Meeting of Optics and the VII Latin American Meeting of Optics, Lasers and Their Applications, edited by Vera L. Brudny, Silvia A. Ledesma, and Mario C. Marconi. SPIE, 2001. http://dx.doi.org/10.1117/12.437182.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Bhardwaj, Anuj, and Anjali Wadhwa. "Medical image enhancement using fractional derivatives." In ADVANCEMENTS IN MATHEMATICS AND ITS EMERGING AREAS. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0003376.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Fractional derivatives' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography