同伦扰动法求解分数阶非线性扩散方程近似解

摘要

Caputo fractional operator is introduced in the diffusion equation with initial condition, and the time-space fractional equation is established. Approximate solution of the fractional nonlinear diffusion equation is obtained by using homotopy perturbation method and mathematica symbols calculation software, and the integer equation is the special case of this fractional equation.%将Caputo分数阶微分算子引入到带有初值条件的扩散方程中,建立了时空分数阶方程.利用同伦扰动法并借助于Mathematica软件的符号计算功能,求解了分数阶非线性扩散方程的近似解,整数阶方程的结果作为特例被包含.