Calculating Resonance Oscillation of Third Order Duffing System with Fractional Order Derivative using the Asymptotic Method

Authors: Nguyen Van Khang*, Bui Thi Thuy, Truong Quoc Chien


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


Fractional-order derivative, Duffing oscillator, Asymptotic method, Harmonic resonance, Amplitude-frequency curves
Pages : 65-69

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