非线性分数阶微分方程的同伦分析解法

Homotopy Analysis Method for Nonlinear Fractional Differential Equation

针对非线性分数阶微分方程的求解问题,提出一种利用同伦分析法(HAM)的近似求解方法 .首先,合理选择辅助参数构建同伦方程.然后,通过构建零阶形变方程和高阶形变方程将原问题分解为多个线性问题,并分别求解.最后,获得在较大范围内收敛的级数解析解.数值实验表明该方法能够有效地求解非线性分数阶微分方程.

For the issue that the solution of nonlinear fractional differential equations,an approximate method based on homotopy analysis method（HAM）is proposed.Firstly,the auxiliary parameters are reasonable chosen according to the problem itself to construct the homotopy equation.Then,the original problem is decomposed into a number of linear problems by constructing the zero order deformation equation and the higher order deformation equation.Finally,the analytic solutions of a wide range of convergent series are obtained.The numerical results show that this method can effectively solve the nonlinear fractional differential equation.