In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral dierential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

Keywords: approximate controllability, semilinear equation, neutral differential equation, local lipschitz continuity, controller operator, reachable set.