Existence and Stability of the Solution to a Coupled System of Fractional-order Differential with a $p$-Laplacian Operator under Boundary Conditions

Abstract

This paper is devoted to studying the uniqueness and existence of the solution to a nonlinear coupled system of (FODEs) with p-Laplacian operator under integral boundary conditions (IBCs). Our problem is based on Caputo fractional derivative of orders $ \sigma,\lambda $, where $ k-1\leq\sigma,\lambda<k, k\geq3$. For these aims, the nonlinear coupled system will be converted into an equivalent integral equations system by the help of Green function. After that, we use Leray-Schauder's and topological degree theorems to prove the existence and uniqueness of the solution. Further, we study certain conditions for the Hyers-Ulam stability of the solution to the suggested problem. We give a suitable and illustrative example as an application of the results.