In this article, the Mittag-Leffler synchronization (MLS) problem of a fractional-order permanent magnet synchronous generator (FOPMSG)-based wind turbine system against unknown disturbances, such as external load torque variations and system parameter uncertainties, an adaptive fractional sliding-mode control (AFSMC) method is proposed based on improved convergence rate performance of the FOPMSG to track accuracy, response speed, and robustness. The AFSMC method is based on a fractional-order term incorporated into the new law for reaching the sliding mode, improves the chattering in the control signal, and reduces the time required for the system to reach the sliding-mode surface. Sufficient conditions are derived to ensure the robust MLS for the sliding-mode dynamics by the designed robust controller. In this article, for the first time, an adaptive sliding-mode control (ASMC) with a terminal function that accurately controls the FOPMSG model at a prespecified time is proposed. Moreover, the designed ASMC can effectively attenuate the existence of disturbances and uncertainties by eliminating the reaching phase based on the Lyapunov stability theory. Finally, the simulation results applied to the FOPMSG model show that the proposed control method has better disturbance rejection ability, fast dynamic response, and suppression of the chattering effect.