This paper deals with the existence of mild solutions for the abstract fractional nonlocal evolution equations with noncompact semigroup in partially ordered Banach spaces. Under some mixed conditions, a group of sufficient conditions for the existence of abstract fractional nonlocal evolution equations are obtained by using a Krasnoselskii type fixed point theorem. The results we obtained are a generalization and continuation of the recent results on this issue. At the end, an example is given to illustrate the applicability of abstract result.
Liang, Y.; Yang, H.; and Gou, Kun, "Existence of Mild Solutions for Fractional Nonlocal Evolution Equations With Delay in Partially Ordered Banach Spaces" (2017). Mathematics Faculty Publications. 1.