Ulam stability of fractional $\psi$-Caputo differential equations involving two orders for fractional derivatives

Abstract

 In the current study, we look at a class of fractional $\psi$-Caputo differential equations having nonlocal boundary integral conditions to investigate both the existence and uniqueness of solutions, using standard fixed point theorems, specifically Banach's fixed point theorem and Krasnoselskii's fixed point theorem. Further, different kinds of Ulam stability have also been studied, particularly Ulam-Hyres stability and Ulam-Hyres-Rassias stability. An example will be given to support the validity of our findings.