Existence and Hyers-Ulam stability of random coupled system of multi-fractional differential equations in generalized Banach space

Abstract

This paper aims to investigate a random coupled system with multiple fractional derivatives of $\psi-$Caputo of different orders subject to non-local integral and boundary condition and proves the uniqueness of random solution by applying random versions of the Pervo fixed point theorem, while the existence of solutions is derived by a random version of a Krasnoselskii-type fixed point theorem. Also, we study the Hyers-Ulam stability of the proposed problem. Obtained results are illustrated by an example.