In this study, a closed-loop Dα -type iterative learning control(ILC) with a proportional D-type iterative learning updating law for the initial shift is applied to nonlinear conformable fractional system. First, the system with the initial shift is introduced. Then, fractional-order ILC (FOILC) frameworks that experience the initial shift problem for the path-tracking of nonlinear conformable fractional order systems are addressed. Moreover, the sufficient condition for the convergence of tracking errors is obtained in the time domain by introducing λ -norm and Hölder’s inequality. Lastly, numerical examples are provided to illustrate the effectiveness of the proposed methods.