关键词: Caputo分数阶微分, 非线性Duffing振子方程, 同伦扰动变换法, 近似解

Abstract: Caputo fractional operator is introduced in the nonlinear Duffing oscillator equation. Homotopy perturbation transform method which is based on homotopy perturbation method and Laplace transform method is applied to solving the fractional nonlinear Duffing oscillator equation and with Mathematica symbols calculation software, the approximate solutions are investigated. The relationship between oscillator movement and fractional derivative is also studied.

Key words: Caputo fractional derivative, nonlinear Duffing oscillator equation, homotopy perturbation transform method, approximate solution