Hyers–Ulam Stability for Fractional Hybrid Switched Systems in Hölder Spaces

This paper establishes a comprehensive theory for fractional hybrid switched differential equations (FHSDEs) in Hölder spaces. We prove the existence of solutions using Schauder’s fixed-point theorem, uniqueness via Banach’s contraction principle, and Hyers-Ulam stability through a direct fixed-point approach. The switched system framework incorporates abrupt changes in fractional dynamics at switching points, while Hölder spaces provide the natural setting for solution regularity. Detailed proofs feature explicit calculations of key constants and inequalities. An illustrative example demonstrates the applicability of our results, including explicit stability constant computations. This work extends hybrid fractional theory to switched systems with Hölder-continuous solutions.