Summary: The classical time domain and frequency domain analysis of Iterative Learning Control (ILC) are extended to a type of time domain analysis of Fractional Order Iterative Learning Control (FOILC) for fractional order nonlinear systems. A novel FOILC scheme is proposed, which leads to a simpler convergence condition. The equivalence of the above two FOILC schemes is shown for the constant learning gain cases, which leads to two further developments: the learnable domain of an adaptive FOILC for the uncertain fractional order systems, and a desirable band-stop FOILC scheme. Several examples are provided to illustrate the presented results.