Existence and Stability Results for Fractional Hybrid Systems with Impulsive Effects

Abstract

This paper investigates the existence and stability of solutions for an impulsive hybrid fractional differential equation involving the Caputo derivative. By extending Dhage’s fixed-point theorem with two operators, we establish solution existence under explicitly derived conditions. Furthermore, we prove Ulam–Hyers stability, providing a quantitative bound that ensures robustness under small perturbations. Two illustrative examples with computed parameter bounds validate the theoretical results and highlight the applicability of the model in real-world systems with abrupt changes and memory effects.