In this paper, based on the previous works, we improve a computational method on solving time-fractional partial differential equation. Using the improved method, a series of time-fractional reaction–diffusion models with Fisher–KPP type are studied from mathematical point of view. Different kinds of exact solutions of four time-fractional reaction–diffusion models are obtained. The forms of these solutions include parametric form, explicit form, and implicit form. Most of them (solutions) have degenerate property according as time increase. The dynamical properties of some representative exact solutions are illustrated by graphs.

中文翻译：

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分离变量法与积分分叉法相结合求解时间分数阶反应扩散模型

本文在先前工作的基础上，对求解时间分数阶偏微分方程的一种计算方法进行了改进。使用改进的方法，从数学的角度研究了一系列Fisher-KPP类型的时间分数反应扩散模型。获得了四种时间分数反应扩散模型的不同精确解。这些解决方案的形式包括参数形式，显式形式和隐式形式。随着时间的增加，它们中的大多数（溶液）都具有退化性质。一些有代表性的精确解的动力学性质由图形表示。