Fixed point theorems in partially ordered Banach spaces with applications to nonlinear fractional evolution equations

摘要

In this paper, a notion of partially Hausdorff measure of noncompactness in partially ordered Banach spaces is introduced, and some Krasnoselskii-type fixed point theorems under certain mixed conditions are proved. Some applications of the obtained fixed point theorems are given to a class of fractional hybrid evolution equations for proving the existence of mild solutions under certain monotonicity conditions. At the end, an example of the fractional parabolic equation is given to illustrate the abstract results.