Relaxation in nonconvex optimal control problems described by evolution Riemann-Liouville fractional differential inclusions

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.