Mild solution in the α-norm for some partial integrodifferential equations involving a nonlocal condition

In this work, we investigate the existence of mild solutions in the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> α -norm for a class of nonlocal integrodifferential equations. We employ the theory of resolvent operators introduced by R. Grimmer. The Leray-Schauder alternative is the principal working tool for our analysis.