Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique

This paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions. Our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point. In addition, the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases: Lipschitz continuous and only continuous, which generalizes the previous contributions. Finally two examples are worked out to illustrate our obtained results.