In this paper the harmonic resonance of third order Duffing oscillator with fractional-order derivative is researched by the asymptotic method. First, the approximately analytical solution and the amplitude-frequency equation are obtained. Based on Liapunov theory, the stability condition of the harmonic solution is also attained. Then, the comparison of the fractional-order and the traditional integer-order of Duffing oscillator is fulfilled by numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied
