Existence, Regularity and Compactness Properties in the $$\alpha $$ α -Norm for Some Partial Functional Integrodifferential Equations with Finite Delay

Abstract

In this work, we study in the \(\alpha \)-norm, the existence, the continuity dependence, regularity and compactness of solutions for some partial functional integro-differential equations by using the operator resolvent theory. We suppose that the linear part has a resolvent operator in the sense of Grimmer and Pritchard (J Diff Equ 50:234–259, 1983). The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. An application is provided to illustrate our results.