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Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces

Mbainadji Djendode

Journal of Applied Analysis

2024

Vol. 30, nr 2

223--237

The purpose of this paper is to study the controllability in the α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach space. To do this, we give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed-point theorem.