Approximate controllability of semi-linear neutral integro-differential systems with finite delay

This paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in Hilbert space. Since the considered equation admits nonlinear terms involving spatial derivatives, the fraction power theory and αα-norm are used to discuss the problem so that the established results can be applied to them. The results are obtained by using the Sadovskii fixed point theorem and the theory of analytic resolvent operator. An example is presented to illustrate the applications of the obtained results.