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Research Article | Open Access

Study of the Atangana-Baleanu-Caputo type fractional system with a generalized Mittag-Leffler kernel

Mdi Begum Jeelani1( ), Abeer S. Alnahdi1, Mohammed A. Almalahi2, Mohammed S. Abdo1,3, Hanan A. Wahash1, M. A. Abdelkawy1,4
Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
Department of Mathematics, Hajjah University, Hajjah, Yemen
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
Department of Mathematics, Faculty of Science, Beni-Seuf University, Beni-Seuf, Egypt
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Abstract

We devote our interest in this work to investigate the sufficient conditions for the existence, uniqueness, and Ulam-Hyers stability of solutions for a new fractional system in the frame of Atangana-Baleanu-Caputo fractional operator with multi-parameters Mittag-Leffler kernels investigated lately by Abdeljawad (Chaos: An Interdisciplinary J. Nonlinear Sci. Vol. 29, no. 2, (2019): 023102). Moreover, the continuous dependence of solution and δ-approximate solutions are analyzed to such a system. Our approach is based on Banach's and Schaefer's fixed point theorems and some mathematical techniques. In order to illustrate the validity of our results, an example is given.

Keywords

generalized Mittag-Lefflergeneralized ABC fractional integrals and derivativesexistencefixed point theoremδ-approximate solution
CLC number: 34A08, 34A12, 34B15, 47H10

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2001-2018
DOI: 10.3934/math.2022115

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Cite this article:
Jeelani MB, Alnahdi AS, Almalahi MA, et al. Study of the Atangana-Baleanu-Caputo type fractional system with a generalized Mittag-Leffler kernel. AIMS Mathematics, 2022, 7(2): 2001-2018. https://doi.org/10.3934/math.2022115

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Received: 08 September 2021
Accepted: 19 October 2021
Published: 15 February 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)