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Research Article | Open Access

An operational calculus formulation of fractional calculus with general analytic kernels

Noosheza Rani, Arran Fernandez( )
Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta, Northern Cyprus, via Mersin-10, Turkey
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Abstract

Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series. We interpret these operators from an algebraic viewpoint, using Mikusiński's operational calculus, and utilise this algebraic formalism to solve some fractional differential equations.

Keywords

fractional integralsfractional derivativesoperational calculusfractional differential equationsMikusiński's operational calculus

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Electronic Research Archive
Volume 30 Issue 12,
December 2022
Pages 4238-4255
DOI: 10.3934/era.2022216

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Cite this article:
Rani N, Fernandez A. An operational calculus formulation of fractional calculus with general analytic kernels. Electronic Research Archive, 2022, 30(12): 4238-4255. https://doi.org/10.3934/era.2022216

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Received: 26 May 2022
Revised: 05 August 2022
Accepted: 31 August 2022
Published: 15 December 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)