Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative

In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations fractional-order with multi-point (discrete) integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder alternative Krasnoselskii’s fixed point theorems used prove solution in first third section. second section emphasizes analysis uniqueness, which is based on Banach theorem’s concept contraction mapping, fourth establishes results. We demonstrate using traditional functional technique. Finally, consequences validated examples.