Controllability in the alpha-norm of Some Impulsive Differential Equation with Infinite delay in Banach Spaces

Abstract

In this work, sufficient conditions for the controllability in the $\alpha$-norm of impulsive  systems with nonlocal conditions with infinite delay are established. We assume that the linear part generates a compact analytic semigroup on a Banach space $X$, the delayed part is assumed to be continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed point theorem.