Study of a class of fractional order non linear neutral abstract Volterra integro-differential equations with deviated arguments

Abstract

In this paper, we give new results on the study of a class of fractional order non linear neutral abstract Volterra integro-differential equations with deviated arguments, considered in a Banach space. Using the method suggested by Hernández et al. (2010), which is based on the theory of resolvent operators for integral equations and fixed point theorems, we prove the main results on the existence and uniqueness of the mild solution of this type of problems which have not been studied before. We also give an example to which our main results are applicable.