By means of the Banach fixed point theorem and the Krasnoselskii’s fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. Results obtained generalize certain earlier results on the fractional equations in the sense of Caputo in Banach spaces under specific conditions. An analytical example is presented to illustrate the concept and detailed solution theorems.

fractional neutral integro-differential equations, initial value problem, Caputo fractional derivative, Krasnoselskii’s fixed point theorem.