Discussion on the Approximate Controllability of Second-Order Neutral Differential Inclusions with Damping

In this paper, the approximate controllability problem is discussed for second-order neutral differential inclusions with damping in Banach spaces. The study establishes the existence of mild solutions for the given system by employing sine and cosine operators and applying Bohnenblust-Karlin’s fixed point theorem for multivalued maps. By introducing a new set of sufficient conditions, it has been proven that the given system is approximately controllable. An example is provided to illustrate the theory.