ABSTRACT

In this paper, we combine the natural transform with the Adomian decomposition for solving nonlinear partial differential equations with time-fractional derivatives. We apply this method to obtain approximate analytical solutions of \((1+n)\)-dimensional fractional Burgers equations. Some illustrative examples are given, which show this to be a very efficient and accurate analytical method for solving nonlinear fractional partial differential equations.

中文翻译：

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用自然分解法求解$$（1 + n）$$（1 + n）-分数阶Burgers方程

摘要

在本文中，我们将自然变换与Adomian分解相结合，以解决带有时间分数导数的非线性偏微分方程。我们应用此方法来获得\（（1 + n）\）-维分数阶Burgers方程的近似解析解。给出了一些说明性示例，这些示例表明这是解决非线性分数阶偏微分方程的一种非常有效且准确的分析方法。