Qualitative Analysis of a Class of Fractional Functional Differential Systems with Feedback Control

In this paper, we investigate a class of fractional functional differential systems with feedback control, in which the fractional derivatives are interpreted in the Caputo sense. By applying Schauder’s fixed point theorem with the Arzelà–Ascoli compactness criterion, we derive existence results for the solutions. Furthermore, specific hypotheses are introduced to establish uniqueness, continuous dependence of the unique solution, and Hyers–Ulam stability of the considered problem. The applicability and relevance of the theoretical results are further demonstrated through several special cases and illustrative examples. The main contribution of this study is to provide a qualitative analysis of a coupled Caputo fractional functional system involving nonlocal integral conditions and feedback control.