This paper presents a new fractional-order control algorithm for a doubly fed induction generator-based wind energy conversion system. Nonlinearities resulting from wind turbine dynamics, parametric uncertainties due to generator modeling, and stochastic wind disturbances can seriously affect control performances and consequently decrease wind power extraction. The suggested approach combines interval type 3 adaptive fuzzy systems with a backstepping control technique to improve the quality of the closed-loop response and the robustness of the system. Besides approximating nonlinear functions, interval type 3 fuzzy systems are used to handle a higher level of uncertainty compared to type 1 or type 2 fuzzy logic approaches. The stability analysis is proved according to the Lyapunov method extended to fractional order. Several simulation results are presented accompanied by a comparative study with some other well-known fuzzy backstepping methods.