Stability and existence results for a system of fractional differential equations via Atangana-Baleanu derivative with \(\phi_{p}\)-Laplacian operator

Volume 27, Issue 2, pp 184--195 http://dx.doi.org/10.22436/jmcs.027.02.08

Publication Date: April 13, 2022 Submission Date: July 26, 2021 Revision Date: October 02, 2021 Accteptance Date: February 15, 2022

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Authors

T. Q. S. Abdullah - School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China. - Department of Mathematics, Faculty of Applied Sciences, Thamar University, Dhamar, Yemen. H. Xiao - School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China. G. Huang - School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China. W. Al-Sadi - School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China.

Abstract

This study focused on the existence and uniqueness(EU) and stability of the solution for a system of fractional differential equations(FDEs) via Atangana-Baleanu derivative in the sense of Caputo (ABC) with \(\phi_{p}\)-Laplacian operator. Green function \( \mathcal{G}^{\eth}(t,s)\), \(m<\eth<m+1\), \(m\geq4\) used for converting the suggested problem to an integral equation. Guo-Krasnoselskii theorem used for proving the EU of solution for the suggested problem. The stability of the solution was derived by Hyers-Ulam stability method(HUS). One illustrative example is used for manifesting the results.

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Keywords

• ABC-Derivative
• Riemann-Liuoville fractional derivative
• Green function
• existence and uniqueness
• Hyers-Ulam stability

MSC

•  34B82
•  26A33
•  45N05

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