Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces

In this paper, we discuss the approximate controllability for a class of retarded semilinear neutral control systems of fractional order by investigating the relations between the reachable set of the semilinear retarded neutral system of fractional order and that of its corresponding linear system. The research direction used here is to find the conditions for nonlinear terms so that controllability is maintained even in perturbations. Finally, we will show a simple example to which the main result can be applied.