Relaxation in control systems of fractional semilinear evolution equations

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.