An Investigation on Existence and Optimal Feedback Control for Fractional Neutral Stochastic Evolution Hemivariational Inequalities

This paper addresses some interesting results of optimal feedback control for neutral stochastic fractional systems in Hilbert spaces. We study the primary results by utilizing the theoretical concepts related to fractional calculus, fixed point theory of multivalued maps, and properties of generalized Clarke’s subdifferential type. Initially, we prove the existence of a mild solution by applying a fixed point technique. Then, we calculate the existence of feasible pair by employing the Filippov theorem and the Cesari property. Also, optimal feedback control results is developed under sufficient conditions. In addition, involving nonlocal conditions for the given control systems is discussed in a separate section. Further, we extend the given control systems with Sobolev-type and the existence of mild solution for the obtained system is evaluated by using the same fixed point theorem. In the end, a simple example is given for the effectiveness of the discussion.