Article
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General Fractional Calculus Operators of Distributed Order
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Version 1
: Received: 3 November 2023 / Approved: 6 November 2023 / Online: 7 November 2023 (08:21:41 CET)
A peer-reviewed article of this Preprint also exists.
Al-Refai, M.; Luchko, Y. General Fractional Calculus Operators of Distributed Order. Axioms 2023, 12, 1075. Al-Refai, M.; Luchko, Y. General Fractional Calculus Operators of Distributed Order. Axioms 2023, 12, 1075.
Abstract
In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.
Keywords
Sonin kernels; Sonin condition; general fractional derivatives; general fractional derivatives of distributed order; fractional integrals of distributed type.
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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