Comparing with the classic phase filed models, the fractional models such as time fractional Allen–Cahn and Cahn–Hilliard equations are equipped with Caputo fractional derivative and can describe more practical phenomena for modeling phase transitions. In this paper, we construct two accurate and efficient linear algorithms for the time fractional Cahn–Hilliard and Allen–Cahn equations with general nonlinear bulk potential. The main contribution is that we have proved the unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn models and their semi‐discrete schemes carefully and rigorously. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of our proposed schemes.

中文翻译：

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精确有效的算法，具有无条件的能量稳定性，适用于时间分数Cahn-Hilliard和Allen-Cahn方程

与经典的相位场模型相比，分数模型（例如时间分数Allen–Cahn和Cahn–Hilliard方程）配备了Caputo分数导数，可以描述用于建模相变的更多实用现象。在本文中，我们为具有一般非线性体势的时间分数Cahn-Hilliard和Allen-Cahn方程构造了两个准确而有效的线性算法。主要的贡献是，我们已经仔细，严格地证明了时间分数Cahn–Hilliard和Allen–Cahn模型及其半离散方案的无条件能量稳定性。演示了2D和3D的几个数值模拟，以验证我们提出的方案的准确性和效率。