On Ulam Stability of Fractional Iterative Differential Equations with Caputo Derivative

Abstract

This work extends stability theory by proving the Hyers–Ulam and Hyers–Ulam–Rassias stability of Caputo fractional iterative differential equations. Using the fixed–point method and a more general form of the Bielecki metric, the study rigorously establishes these stability results. It examines both bounded and unbounded intervals and provides examples to demonstrate the effectiveness of the proposed theoretical results.