Controllability for a class of semilinear fractional evolution systems via resolvent operators

This paper deals with the exact controllability for a class of fractional evolution systems in a Banach space. First, we introduce a new concept of exact controllability and give notion of the mild solutions of the considered evolutional systems via resolvent operators. Second, by utilizing the semigroup theory, the fixed point strategy and Kuratowski's measure of noncompactness, the exact controllability of the evolutional systems is investigated without Lipschitz continuity and growth conditions imposed on nonlinear functions. The results are established under the hypothesis that the resolvent operator is differentiable and analytic, respectively, instead of supposing that the semigroup is compact. An example is provided to illustrate the proposed results.