Some results, in the α-norm, for nonlinear integro-differential equations with finite delay

Abstract

In this paper, we consider, in a general Banach space, a nonlinear integro-differential equation with finite delay. The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. Using the semigroup theory, we prove some qualitative and quantitative results under the alpha norm. An application is provided to illustrate our results.