Abstract: We considered the periodic problem of a class of nonlinear iterative differential equation in the sense of Caputo type fractional derivative. Under one sided-Lipschtiz conditions on nonlinear term, the existence and uniqueness of solution for the nonlinear fractional iterative differential equations is proved by applying the Leray-Schauder fixed point theorem and topological degree theory.

Key words: existence, uniqueness, fractional order, iterative equation