A Novel Approach to Nonlinear Fractional Volterra-Fredholm Integro-Differential Equations via Caputo-Katugampola Operators

Abstract

This paper aims to examine the solvability, uniqueness, and stability of a class of nonlinear implicit fractional Volterra-Fredholm integrodifferential equations involving the Caputo-Katugampola fractional derivative. The main objective is to establish rigorous conditions under which such equations admit unique solutions and to analyze their stability behavior under perturbations. Specifically, we apply Banach’s fixed-point theorem and a suitable form of the Gronwall inequality to derive sufficient criteria for existence and uniqueness. Furthermore, we investigate the stability of solutions in the sense of Ulam-Hyers and Ulam-Hyers-Rassias, providing a comprehensive understanding of the solution behavior under small deviations. To validate the theoretical results and highlight the applicability of the developed framework, a concrete illustrative example is included. This study contributes to the ongoing development of fractional calculus by deepening the theoretical understanding of fractional integrodifferential equations and expanding their potential for modeling complex dynamical systems in various applied sciences.OPEN ACCESS Received: 02/05/2025 Accepted: 19/06/2025 Published: 15/08/2025

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