Summary: We discuss double perturbed neutral functional evolution equation with infinite delay
where is a family of linear closed operators in a real Banach space that generates an evolution system and is dense in . The history , , belongs to some abstract phase space defined axiomatically; are appropriate functions.
The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and a fixed point theorem, without the compactness assumption on the associated evolution system. Our results improve and generalize some previous results.