Results 11 to 20 of about 40,668 (308)
A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions [PDF]
Abstract and Applied Analysis, 2013 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 ...
Abdon Atangana, Aydin Secer
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A Factory of Fractional Derivatives [PDF]
SymmetryThis paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken.
Manuel D. Ortigueira +1 more
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Opial type Lp-inequalities for fractional derivatives [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of
G. A. Anastassiou +2 more
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On the fractional deformation of a linearly elastic bar
Journal of the Mechanical Behavior of Materials, 2020 Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local ...
Lazopoulos Konstantinos A. +1 more
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Journal of Advanced Research, 2023 Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari +2 more
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Mathematics, 2021 In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator.
Fátima Cruz +2 more
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International Journal of Analysis and Applications, 2023 This study presents the fractional reduced differential transform method for a nonlinear mutualism model with fractional diffusion. The fractional derivatives are described by Caputo's fractional operator.
Mohamed Ahmed Abdallah +1 more
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FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE [PDF]
International Journal of Mathematics, 2007 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.
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Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Some types of first order fractional differential equations and their applications [PDF]
E3S Web of Conferences, 2021 This paper uses a new multiplication of fractional functions and chain rule for fractional derivatives, regarding the Jumarie type of modified Riemann-Liouville fractional derivatives to obtain the general solutions of four types of first order ...
Yu Chiihuei
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