Existence Results for Fractional Neutral Functional Integro-Differential Evolution Equations With Infinite Delay in Banach Spaces

Abstract

In this paper, we investigate the existence results for a class of abstract fractional neutral integro-differential evolution systems involving the Caputo derivative in Banach spaces. The main techniques rely on the fractional calculus, properties of characteristic solution operators, Monch's fixed point theorem via measures of noncompactness. Particularly, we do not assume that characteristic solution operators are compact. The application is given to illustrate the theory. The results of this article are generalization and improvement of the recent results on this issue. MSC: 26A33, 34A12, 47H08, 47H10.