Abstract: A novel method which is based on variational iteration method, Laplace transform and homotopy perturbation method is proposed, and this new method is applied to obtain the approximate solutions of the fractional coupled MKdV equation. The fractional Lagrange multiplier is accurately determined by the Laplace transform and the nonlinear term can be easily handled by He’s polynomials. The results demonstrate accuracy and fast convergence of this new algorithm.

Key words: variational iteration method, Laplace transform, homotopy perturbation method, fractional equation, nonlinear equation

摘要： 将变分迭代法、同伦扰动法和Laplace变换相结合应用于分数阶非线性发展方程近似解的求解，其中Laplace变换可准确方便地求得分数阶的Lagrange乘子，而He的多项式可简单地处理方程中出现的非线性项，将新的处理方法应用到分数阶耦合的MKdV方程，结果表明该方法具有较高的精度和收敛性。

关键词: 变分迭代法, Laplace变换, 同伦扰动法, 分数阶方程, 非线性方程