This study is devoted to the analysis of feedback control problems for a class of fractional hemivariational inequalities of order \(1< \zeta <2\) with finite delay. The proposed framework integrates techniques from fractional calculus, cosine operator theory, mild solutions, multivalued analysis, Clarke’s subdifferential, and the Bohnenblust-Karlin’s fixed point theorem to establish the theoretical results. First, sufficient conditions ensuring the existence of mild solutions to the considered system are derived. Building on these results, the concept of feasible pairs is introduced, providing an analytical foundation for the formulation and proof of the existence of optimal feedback control. Moreover, the structure of the associated feedback control pairs is characterized, highlighting their role in governing delayed fractional systems with nonsmooth and nonconvex dynamics. Finally, an illustrative example is presented to demonstrate the applicability and effectiveness of the developed theoretical framework.
