On the Generalized Ulam–Hyers Stability for Caputo Fractional Derivatives with Nonlocal Conditions

This paper addresses the need for rigorous stability criteria in fractional integro-differential systems by investigating generalized Ulam–Hyers stability for equations involving a fractional-order derivative. The research objective is to establish sufficient conditions that guarantee generalized Ulam–Hyers stability for Caputo fractional differential equations. Methodologically, the study employs concise mathematical arguments together with an application of the Gronwall inequality to derive the required conditions. The key findings demonstrate that these conditions ensure stability in the generalized Ulam–Hyers sense for the considered class of equations. The paper concludes that the obtained results extend and improve upon existing findings in the literature. The contribution lies in refining the stability theory for fractional-order models by providing tractable criteria grounded in Gronwall-type estimates and Caputo derivatives.