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Research Article | Open Access

Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel

Mohamed I. Abbas1, Maria Alessandra Ragusa2( )
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
Dipartimento di Matematica e Informatica, Università di Catania; RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russia
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Abstract

In the existing article, the existence of solutions to nonlinear fractional differential inclusions in the sense of the Atangana-Baleanu-Caputo ( A B C ) fractional derivatives in Banach space is studied. The investigation of the main results relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness. A simulated example is proposed to explain the obtained results.

Keywords

Atangana-Baleanu fractional derivativesmeasure of non-compactnessMönch fixed point theorem
CLC number: 35J10, 35C08, 35A18, 34A08

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AIMS Mathematics
Volume 7 Issue 11,
November 2022
Pages 20328-20340
DOI: 10.3934/math.20221113

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Cite this article:
Abbas MI, Ragusa MA. Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel. AIMS Mathematics, 2022, 7(11): 20328-20340. https://doi.org/10.3934/math.20221113

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Received: 12 August 2022
Revised: 04 September 2022
Accepted: 14 September 2022
Published: 15 November 2022
©2022 the Author(s), licensee AIMS Press.

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