Time-optimal feedback control of nonlocal Hilfer fractional state-dependent delay inclusion with Clarke's subdifferential

In this article, we discuss the optimal feedback control of nonlocal Hilfer fractional state-dependent delay inclusion of order 1 < alpha < 2 with Clarke's subdifferential. Firstly, we establish the existence of mild solutions for this class of equations by employing the Krasnoselskii's fixed-point theorem, without using Lipschitz conditions. Subsequently, we develop set of sufficient assumptions, utilizing Cesari property and Filippov theorem, to ensure the existence of feasible pairs for the feedback control systems. Eventually, using the Mazur theorem and Fatou's lemma, we derive the optimal state-control pair. The study also introduces and explores the problem of time-optimal feedback control. In conclusion, an application is provided to enhance the theoretical findings.