Exploration of Ulam-Hyers stability for a system of fractional integro

This study examines existence, uniqueness, and Ulam-Hyers stability for solutions of nonlinear coupled fractional integro-differential equations with integral boundary conditions.Fractional systems incorporating memory and hereditary effects serve as effective models for complex processes in science and engineering applications.This study proves solution existence and uniqueness by applying the Banach fixed-point theorem within carefully constructed function spaces, then extends our analysis to investigate Ulam-Hyers stability, a framework that reveals how solutions behave when initial conditions contain small errors.Our stability analysis demonstrates that minor perturbations in starting data translate to bounded solution variations, keeping the system stable within predictable limits, which we verify through a computational example showing how controlled initial changes produce correspondingly controlled solution deviations.These results advance stability theory for coupled fractional integro-differential systems, particularly where memory effects influence system behavior, mathematical models that appear frequently in applications ranging from viscoelastic materials to population dynamics, where past states influence current evolution.By establishing rigorous stability bounds, our work provides a theoretical foundation for implementing these models in real-world scenarios where measurement uncertainties and modeling approximations are inevitable.