Fractional Derivatives Application to Image Fusion Problems [PDF]
Sensors, 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 ...
Szymon Motłoch +2 more
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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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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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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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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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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 Multifractality and Fractional Derivatives [PDF]
Journal of Statistical Physics, 2002 It is shown phenomenologically that the fractional derivative $ξ=D^αu$ of order $α$ of a multifractal function has a power-law tail $\propto |ξ| ^{-p_\star}$ in its cumulative probability, for a suitable range of $α$'s. The exponent is determined by the condition $ζ_{p_\star} = αp_\star$, where $ζ_p$ is the exponent of the structure function of order ...
U. Frisch, T. Matsumoto
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