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This paper derives a nonlinear translational and rotational dynamic model of the quadrotor UAV. An original fractional-order backstepping sliding mode control method for a typical quadrotor UAV is presented. The new approach can decrease the chattering phenomenon and increase the robustness of control strategy. The strongly coupled characteristics of the under-actuated system are sought by the virtual controllers. The feasibility for different track trajectories are verified using MATLAB. The new control method can not only track the expected trajectory very well but also has a better robustness for different complex trajectory under disturbances, as the simulation results demonstrate.