Results 11 to 20 of about 487,487 (101)

Multi-Kernel General Fractional Calculus of Arbitrary Order

Mathematics, 2023
An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels are used.
Vasily E. Tarasov
doaj   +3 more sources

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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Nonlocal Probability Theory: General Fractional Calculus Approach

Mathematics, 2022
Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of ...
Vasily E. Tarasov
doaj   +2 more sources

General Fractional Integrals and Derivatives with the Sonine Kernels [PDF]

Mathematics, 2021
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed.
Yuri Luchko
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General Fractional q-Integrals and q-Derivatives: A Sonin–Luchko q-Kernel Approach

Arabian Journal of Mathematics
Fethi Bouzeffour
exaly   +3 more sources

Symmetrical Sonin kernels in terms of the hypergeometric functions [PDF]

, 2023
In this paper, we introduce a new class of the kernels of the integral transforms of the Laplace convolution type that we call symmetrical Sonin kernels. For a symmetrical Sonin kernel given in terms of some elementary or special functions, its associated kernel has the same form with possibly different parameter values.
Luchko, Yuri
core   +4 more sources

Generalising the fractional calculus with Sonine kernels via conjugations

Journal of Computational and Applied Mathematics, 2023
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Mohammed Al-Refai, Arran Fernandez
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On an Analogy of Fermat’s Theorem for the First-Level General Fractional Derivative and Its Applications

Fractal and Fractional
Fermat’s theorem, often referred to as the interior extrema theorem, is one of the fundamental results in calculus and optimization theory. Recently, the statement of this theorem has been generalized to the case of fractional derivatives.
Mohammed Al-Refai, Yuri Luchko
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A Tempered Fractional Diffusion Equation With Sonin Kernel as Anomalous Diffusion Model

Communications in Nonlinear Science and Numerical Simulation
Yuri Luchko
exaly   +3 more sources

Extending Sonine kernels to arbitrary dimensions

Banach Journal of Mathematical Analysis
Abstract The theory of general fractional calculus with Sonine kernels has been well developed by Luchko in the one-dimensional case. Inspired by recent work on Mikusiński’s operational calculus for fractional partial differential operators, we construct a multi-dimensional version of the theory of Sonine kernels, solving a recognised open ...
A. Fernandez
openaire   +2 more sources