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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]

We are concerned with control systems described by a class of semilinear fractional evolution hemivariational inequalities in separable reflexive Banach spaces. The constraint on the control is a nonconvex valued multivalued function which is lower semicontinuous with respect to the variable states. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex valued regularization of the original constraint. We obtain the existence results of the control systems and the relaxation property among the solution sets of these systems. In the end, an example is provided to illustrate the application of the obtained theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a control system of nonlinear evolution hemivariational inequalities with mixed nonconvex constraints on the control. First, we investigate the relaxed problem for the hemivariational inequalities systems with feedback control and the integrand convexicated with respect to the control. Second, under some general conditions, the existence of optimal solution of the relaxed problem for hemivariational inequalities control systems is proved. Furthermore, we show that for every optimal solution there exists a minimizing sequence of the original problem converging to the optimal solution with respect to trajectories and the functional in appropriate topologies simultaneously. Finally, an example is provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

A control system described by fractional evolution integro-differential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems.

We consider a control system described by fractional semilinear evolution equations with a mixed multivalued control constraint whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraint on the control is the closed convex hull of the original constraint. We obtain existence results for the control systems and study relations between the solution sets of the two systems. An example is given to illustrate the abstract results.

A control system described by fractional evolution integro-differ-ential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems. [ABSTRACT FROM AUTHOR]

Abstract: We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is 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. [Copyright &y& Elsevier]