Existence of positive solutions for fractional delayed evolution equations of order \(\gamma \in (1,2)\) via measure of non-compactness

The purpose of this paper is to consider the fractional delayed evolution equation of order \(\gamma \in (1,2)\) $\gamma \in (1,2)$ in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear function satisfies the non-compactness measure conditions and some appropriate growth conditions or order conditions.