Nonlocal Fractional Hahn Integral Conditions in Sequential Nonlinear Integro-Difference Equations: Existence and Stability Perspectives

Abstract

In this paper, we investigate the existence, uniqueness, and stability of solutions for a class of sequential fractional Hahn integro-difference boundary value problems. To facilitate the analysis, several key properties of the fractional Hahn integral are derived and utilized as computational tools. The considered problem involves a combination of three distinct fractional Hahn difference operators together with two fractional Hahn integrals of varying orders, which provides a richer framework than existing studies. By applying both the Banach fixed point theorem and the Schauder fixed point theorem, we establish rigorous conditions ensuring the existence and uniqueness of solutions. Furthermore, we demonstrate the Hyers–Ulam stability of the proposed model, highlighting its robustness under perturbations. An illustrative example is also provided to confirm the effectiveness and applicability of the theoretical results.