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 Application to Image Fusion Problems. [PDF]
Sensors (Basel), 2022 In this paper, an analysis of the method that uses a fractional order calculus to multispectral images fusion is presented. We analyze some correct basic definitions of the fractional order derivatives that are used in the image processing context ...
Motłoch S, Sarwas G, Dzieliński A.
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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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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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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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On Λ-Fractional Analysis and Mechanics
Axioms, 2022 Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology.
Konstantinos A. Lazopoulos
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How Many Fractional Derivatives Are There?
Mathematics, 2022 In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained.
Duarte Valério +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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