Abstract
In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order beta is an element of (1, 2] subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous beta-order fractional cosine family, while the nonlinear forcing term is of Caratheodory type and satisfies some fairly general growth conditions. Our approach combines the Monch fixed point theorem with some recent results regarding the measure of noncompactness of integral operators. Our conclusions improve and generalize many earlier related works. An example is provided to illustrate the main results.