This study focuses on implementing consensus track-ing using both open-loop and closed-loop Dα-type iterative learning control (ILC) schemes, for fractional-order multi-agent systems (FOMASs) with state-delays. The desired trajectory is constructed by introducing a virtual leader, and the fixed com-munication topology is considered and only a subset of follow-ers can access the desired trajectory. For each control scheme, one controller is designed for one agent individually. According to the tracking error between the agent and the virtual leader, and the tracking errors between the agent and neighboring agents during the last iteration (for open-loop scheme) or the current running (for closed-loop scheme), each controller con-tinuously corrects the last control law by a combination of com-munication weights in the topology to obtain the ideal control law. Through the rigorous analysis, sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time interval. Sufficient numerical simulation results demonstrate the effectiveness of the control schemes, and provide some meaningful comparison results.