Approximate controllability of semilinear system involving state-dependent delay via fundamental solution

This article studies approximate controllability for a new class of semilinear control systems involving state-dependent delay in Hilbert space setting. We formulate some new sufficient conditions which ensure the existence of mild solution for the considered system via the Schauder fixed point theorem. We use the theory of fundamental solution and fractional powers of operator, to establish our major results. At last, two examples are constructed to substantiate the application of obtained results.