Energy ripples are among the common problems in renewable energies as a result of using less efficient strategies. In this work, a new technique is suggested to control a doubly-fed induction generator (DFIG) using the pulse width modulation (PWM). The new technique is based on the combination of neural networks and fractional-order control to minimize the reactive and active power ripples of the DFIG-based variable speed dual-rotor wind turbine system. The suggested fractional-order neural control (FONC) with the PWM is a simple, robust and a high-performance strategy. Simulation is performed using Matlab software to validate the effectiveness of the designed control of 1.5 MW DFIG and the obtained results are compared with the traditional direct power control (DPC) in different working conditions. In addition, the comparison between the suggested control and the DPC is performed in the cases of changing or not changing the device parameters in terms of ripple ratio, dynamic response, steady-state error, current quality, and overshoot of active and reactive power of the DFIG. As compared to the DPC, the proposed FONC technique improves the active and reactive power ripples by 65.71% and 84.74%, respectively. Also, improves the overshoot of the active and reactive power by 71.33% and 91.72%, respectively. The simulation results demonstrate the high performance and robustness of the FONC technique for the parametric variations of the DFIG-based variable speed dual-rotor wind turbine system compared to the DPC control.