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 integrand that is not convex in control on solutions a Riemann-Liouville fractional differential system mixed nonconvex feedback constraints control. At First, existence results for semilinear systems discussed by using Schauder's fixed point theorem. Under some reasonable assumptions, prove relaxation has optimal solution, and each solution there minimizing sequence original converges to respect trajectory, control, appropriate topologies simultaneously. Finally, give example illustrate our main results.