Abstract
In this study, we examine the existence and Hyers-Ulam stability of a coupled system of generalized Liouville-Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray-Schauder alternative and Krasnoselskii's fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem's concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers-Ulam stability are established in the next theorem. We establish the stability of Ulam-Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville-Caputo (rho) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic.