On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions

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