Controllability results in α-norm for some partial functional integrodifferential equations with infinite delay in Banach spaces

Abstract

This work concerns the controllability in the α-norm for some partial functional integrodifferential equations with infinite delay in Banach spaces. We give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer [7] and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained using the Schauder’s fixed-point theorem.