Fixed Point Theorems via MNC in Ordered Banach Space with Application to Fractional Integro-differential Evolution Equations

Abstract

In this paper, we propose fixed point results through the notion of measure of noncompactness (MNC) in partially ordered Banach spaces. We also prove some new coupled fixed point results via MNC for more general class of function. To achieve this result, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. Further, we apply the obtained fixed point theorems to prove the existence of mild solutions for fractional integro-differential evolution equations with nonlocal conditions. At the end, an example is given to illustrate the rationality of the abstract results for fractional parabolic equations.