Solvability and stability analysis of a coupled system involving generalized fractional derivatives

Abstract

In this article, we investigate the existence of unique maximal and minimal solutions for a coupled differential system in terms of generalized fractional derivative with arbitrary order. The iterative technique of a fixed point operator together with the properties of green's function are used basically. Moreover, we investigate the generalized Ulam-Hyers stability of the solution for the given coupled system. Finally, some examples are given to illustrate the theoretic results.

Keywords

• existence and uniqueness
• generalized fractional derivative and integral
• boundary value problem
• minimal and maximal solutions
• ulam-hyers