OPTIMAL CONTROLS FOR MULTITERM FRACTIONAL EVOLUTION EQUATIONS OF SOBOLEV TYPE

We investigate time-optimal controls invoked by Sobolev-type multiterm time fractional differential equations in new forms. We prove the existence of mild solutions of Sobolev type multiterm time-fractional evolution equations in the Caputo and Riemann–Liouville fractional derivatives; then we investigate time-optimal control of such systems. Our results fall under the framework of the resolvent operator family related to the Sobolev-type fractional evolution equations. The uniqueness of solutions and the reflexivity of the state-valued space are not required for time-optimal control problems.