Existence, uniqueness, and stability of solutions for nonlinear fractional integro-differential equations with nonlocal boundary conditions and fractional derivatives

Abstract

This study investigates a nonlinear fractional integro-differential equation defined by Riemann-Liouville fractional derivatives, focusing on the existence, uniqueness, and stability of its solutions. Using advanced fixed-point theorems, specifically the Banach and Krasnoselskii’s fixed-point theorems, we derive precise conditions for the existence and uniqueness of solutions. We also conduct a stability analysis, establishing criteria to ensure the robustness of solutions under minor perturbations. The theoretical results extend existing frameworks in fractional differential equations and provide novel insights into fractional dynamic systems. To validate our theoretical findings and demonstrate their practical applicability, we present a numerical example that illustrates the solution behavior under varying fractional orders, nonlinearities, and boundary conditions. This example highlights the effectiveness of the proposed methods and lays the foundation for future research on fractional integro-differential equations in real-world applications.