EXISTENCE AND STABILITY RESULTS FOR COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING AB-CAPUTO DERIVATIVE
Nayyar Mehmood, AHSAN ABBAS, Ali Akgül, Thabet Abdeljawad, Manar A. Alqudah
Abstract
In this paper, we use Krasnoselskii’s fixed point theorem to find existence results for the solution of the following nonlinear fractional differential equations (FDEs) for a coupled system involving AB-Caputo fractional derivative [Formula: see text] with boundary conditions [Formula: see text] We discuss uniqueness with the help of the Banach contraction principle. The criteria for Hyers–Ulam stability of given AB-Caputo fractional-coupled boundary value problem (BVP) is also discussed. Some examples are provided to validate our results. In Example 1, we find a unique and stable solution of AB-Caputo fractional-coupled BVP. In Example 2, the analysis of approximate and exact solutions with errors of nonlinear integral equations is elaborated with graphs.