Hilfer–Katugampola fractional derivatives
Computational and Applied Mathematics, 2017 We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type.
Oliveira, D. S., de Oliveira, E. Capelas
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Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula
Journal of Inequalities and ApplicationsIn this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden +3 more
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A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions
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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Fractional Liouville Equation on Lattice Phase-Space
, 2015 In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested.
Tarasov, Vasily E.
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A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String [PDF]
, 2010 We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the
Almeida, Ricardo +2 more
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Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial
Mathematics, 2019 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.
Roberto Garrappa +2 more
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Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory
Mathematics, 2022 For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces.
Masahiro Yamamoto
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Holder exponents of irregular signals and local fractional derivatives
, 1997 It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations.
A Arneodo +69 more
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Analysis of Drude model using fractional derivatives without singular kernels
Open Physics, 2017 We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffler function.
Jiménez Leonardo Martínez +3 more
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Two Integral Representations for the Relaxation Modulus of the Generalized Fractional Zener Model
Fractal and Fractional, 2023 A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying the
Emilia Bazhlekova, Sergey Pshenichnov
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