A Study on Controllability and Periodicity Solutions for Nonlinear Neutral Integrodifferential System

Abstract

The objective of this paper is to present sufficient conditions for controllability and periodicity solutions of an integrodifferential system in Banach space. The main results are obtained by using resolvent operators and a fixed point approach. Further, the mild solution of the integrodifferential system has been shown to be compact asymptotically almost automorphic . Then uniqueness of the asymptotically almost automorphic solution has been shown by the Banach contraction principle. Finally, an example is provided to show the effectiveness of the obtained theoretical result.