In this paper, we investigate the exact solutions of the generalized time fractional foam drainage equation. The Lie-group scaling transformation method and improved [Formula: see text]-expansion method are adopted here. The equation describes the evolution of the vertical density profile of a foam under gravity. New exact solutions and maple diagrams of the generalized time fractional foam drainage equation can help us better understand the physical phenomena.

中文翻译：

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广义时间分数泡沫排水方程的多重精确解

在本文中，我们研究了广义时间分数式泡沫排水方程的精确解。这里采用李群标度变换法和改进的[公式：见正文]-展开法。该方程描述了泡沫在重力作用下的垂直密度分布的演变。广义时间分数式泡沫排水方程的新精确解和枫图可以帮助我们更好地理解物理现象。