No nonlocality. No fractional derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2018 The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point.
Vasily E. Tarasov
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Fractional Derivatives: The Perspective of System Theory
Mathematics, 2019 This paper addresses the present day problem of multiple proposals for operators under the umbrella of “fractional derivatives„. Several papers demonstrated that various of those “novel„ definitions are incorrect.
Manuel Duarte Ortigueira +1 more
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On fractional derivatives with generalized Mittag-Leffler kernels
Advances in Difference Equations, 2018 Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms.
Thabet Abdeljawad, Dumitru Baleanu
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The mathematical description of the bulk fluid flow and that of the content impurity dispersion, obtained by replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective [PDF]
INCAS Bulletin, 2021 In the field of fractional calculus applications, there is a tendency to admit that “integer-order derivatives cannot simply be replaced by fractional-order derivatives to develop fractional-order theories”.
Agneta M. BALINT, Stefan BALINT
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THE 1ST LEVEL GENERAL FRACTIONAL DERIVATIVES AND SOME OF THEIR PROPERTIES [PDF]
Journal of Mathematical Sciences, 2022 In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far.
Yuri Luchko
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Bilateral Tempered Fractional Derivatives [PDF]
Symmetry, 2021 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 showed that it cannot be considered as a derivative.
Manuel Duarte Ortigueira +1 more
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General Fractional Calculus Operators of Distributed Order
Axioms, 2023 In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
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A New Class of Generalized Fractal and Fractal-Fractional Derivatives with Non-Singular Kernels
Fractal and Fractional, 2023 The present paper introduces a new class of generalized differential and integral operators. This class includes and generalizes a large number of definitions of fractal-fractional derivatives and integral operators used to model the complex dynamics of ...
K. Hattaf
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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
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