This article deals with a novel fractional-order active disturbance rejection control (FADRC) scheme to handle a general integer-order system. The proposed control structure enhances the robustness and performance of the classical active disturbance rejection control, especially for the open-loop gain variation. Based on the Bode's ideal transfer function, an analytical design of a state-feedback control is proposed. The integer-order model of the system to be controlled is first transformed to a noninteger-order one, where the introduced fractional order is a design parameter, which imposes the overshoot of the closed-loop step response. In addition, because the model of the system is transformed to a cascade of integer- and fractional-order integrator (the model is noncommensurate), a commensurate fractional-order extended state observer is proposed to estimate the generalized disturbance. To improve the robustness of the proposed FADRC scheme, an analytical design method of a noncommensurate state-feedback control is proposed. The proposed design method is based on the Bode's ideal transfer function cascaded with an integer-order filter. The proposed FADRC scheme is applied for a pendulum-cart test bed, and the effectiveness and robustness of the proposed control are examined by experiments.