Controllability of Damped Second Order Semi-linear Neutral Functional Differential Inclusions in Banach Spaces

In this article, we investigate sufficient conditions for controllability of second-order semi-linear damped neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work is motivated by the paper of Benchohra, Gorniewicz and Ntouyas [1] and extends the work of Chalishajar [2].