Approximate Controllability for a Kind of Fractional Neutral Differential Equations with Damping

This paper gains several meaningful results on the mild solutions and approximate controllability for a kind of fractional neutral differential equations with damping (FNDED) and order belonging to in Banach spaces. At first, a new expression for the mild solutions of FNDED via the (p, q)-regularized operator family and the technique of Laplace transform is acquired. Then, we consider the approximate controllability of FNDED by means of the approximate sequence method, and simultaneously, some applicable sufficient conditions are obtained.