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

• Published in: AIMS mathematics Vol. 7; no. 2; pp. 2001 - 2018
• Main Authors: Jeelani, Mdi Begum, Alnahdi, Abeer S., Almalahi, Mohammed A., Abdo, Mohammed S., Wahash, Hanan A., Abdelkawy, M. A.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: existence; fixed point theorem; generalized abc fractional integrals and derivatives; generalized mittag-leffler; δ-approximate solution
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022115

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.