RELAXATION IN NONCONVEX OPTIMAL CONTROL PROBLEMS FOR NONAUTONOMOUS FRACTIONAL EVOLUTION EQUATIONS

We deal with the minimization problem of an integral functional with an integrand that is not convex in the control, on solutions of a control system described by a nonautonomous fractional evolution equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that 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.