This work aims to investigate the existence and uniqueness of the solutions to fractional order nonlinear abstract Volterra-Fredholm integro-differential equations with deviated argument, considered in a Banach space and in a non-autonomous case. Using the method proposed by Hernández et al. [17], which is based on the theory of resolvent operators for integral equations and fixed point theorems, we prove new results on the existence and uniqueness of the mild solution of this type of problems which have not been studied previously. We also give an example illustrating our main results.