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

摘要： 将Caputo分数阶微分算子引入到非线性的Duffing振子方程中，运用同伦扰动变换法——一种同伦扰动法和Laplace变换相结合的方法来求解分数阶的非线性方程，借助Mathematica软件的符号计算功能得到了分数阶非线性Duffing振子方程的近似解，研究了振子运动过程与分数阶导数之间的关系。

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