Controllability of Sobolev Type Fractional Evolution Systems

The main purpose of this paper is to investigate a class of Sobolev type semilinear fractional evolution systems in a separable Banach space. Applying a suitable fixed point theorem as well as condensing mapping, controllability results for two class of control sets are established by means of the theory of propagation family and technique of measure of noncompactness. An application involving a partial differential equation with a Caupto fractional derivative is considered.