This study examines the existence and optimal control for a class of non-autonomous fractional differential systems of order \(\alpha \in (1,2)\) , constrained by nonlocal initial conditions. The system is governed by the Caputo fractional derivative, and significantly, no Lipschitz requirement is enforced on the nonlinear term, thus expanding the applicability of the results to a wider range of systems. Using Schauder’s fixed point theorem, the existence of mild solutions is shown in the framework of fractional evolution families. Additionally, the method of minimizing sequences is utilized to prove that there exists an optimal control that optimizes a certain performance index. This article provides an example to demonstrate the practical relevance of the theoretical findings.
