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The goal of this article considers a class of semilinear fractional evolution hemivariational inequalities control systems described by the Riemann-Liouville fractional derivative in separable reflexive Banach spaces. At first, the existence of Riemann-Liouville fractional semilinear evolution hemivariational inequalities with nonconvex feedback control constraint is discussed by applying fractional operator theory and Schauder's fixed point theorem. Then, we show that the set of the original system's trajectories can be approximated by the set of the upper semicontinuous convex valued regularization of the original feedback system's trajectories under certain hypotheses. Also, an example is given to illustrate our main results at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a Riemann-Liouville fractional differential control system with mixed nonconvex feedback constraints on the control. At First, the existence results for Riemann-Liouville fractional semilinear differential control systems are discussed by using Schauder's fixed point theorem. Under some reasonable assumptions, we prove that the relaxation problem has an optimal solution, and that for each optimal solution there has a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously. Finally, we give an example to illustrate our main results. [ABSTRACT FROM AUTHOR]