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

Mdi Begum Jeelani; Abeer S. Alnahdi; Mohammed A. Almalahi; Mohammed S. Abdo; Hanan A. Wahash; M. A. Abdelkawy; Mdi Begum Jeelani; Abeer S. Alnahdi; Mohammed A. Almalahi; Mohammed S. Abdo; Hanan A. Wahash; M. A. Abdelkawy

doi:10.3934/math.2022115

AIMS Mathematics

2022, Volume 7, Issue 2: 2001-2018. doi: 10.3934/math.2022115

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Research article

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

1.
Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
2.
Department of Mathematics, Hajjah University, Hajjah, Yemen
3.
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
4.
Department of Mathematics, Faculty of Science, Beni-Seuf University, Beni-Seuf, Egypt
5.
Department of Mathematics, Dr.Babasaheb Ambedkar Marathwada University, Aurangabad, India
Correction on: AIMS Mathematics 7: 20543-20544

Received: 08 September 2021 Accepted: 19 October 2021 Published: 05 November 2021
MSC : 34A08, 34A12, 34B15, 47H10

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 $ \delta $-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.
- generalized Mittag-Leffler,
- generalized ABC fractional integrals and derivatives,
- existence,
- fixed point theorem,
- $ \delta $-approximate solution
Citation: Mdi Begum Jeelani, Abeer S. Alnahdi, Mohammed A. Almalahi, Mohammed S. Abdo, Hanan A. Wahash, M. A. Abdelkawy. Study of the Atangana-Baleanu-Caputo type fractional system with a generalized Mittag-Leffler kernel[J]. AIMS Mathematics, 2022, 7(2): 2001-2018. doi: 10.3934/math.2022115

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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 $ \delta $-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.

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