Controllability of nonlocal fractional functional differential equations of neutral type in a Banach space

Abstract

This paper is concerned with the controllability of nonlinear nonlocal fractional neutral functional evolution system in a Banach space. Sufficient conditions are obtained by using Krasnoselskii's fixed point theorem and semigroup theory. In particular, we assume that the nonlinear parts satisfy locally Lipschitz like conditions and closed linear (not necessarily bounded) operator −A(t) generates analytic semigroup for each t ≥ 0. We also investigate null controllability of the considered system. An example is given to illustrate the effectiveness of our results.