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

Abstract

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

Keywords

• generalized Liouville–Caputo derivatives
• generalized fractional integrals
• multi- points
• coupled system
• existence
• fixed point