Based on the \(\tan (\Phi (\xi )/2)\)-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.

中文翻译：

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应用$$ \ tan（\ Phi（\ xi）/ 2）$$ tan（Φ（ξ）/ 2）-展开法求解某些非线性分数物理模型

基于\（\ tan（\ Phi（\ xi）/ 2）\）-展开方法，研究了五个非线性分数物理模型，以获得包含三种类型的双曲函数，三角函数和有理函数解的解。这些方程是时间分数生物种群模型，时间分数Burgers，时间分数Cahn–Hilliard，时空分数Whitham–Broer–Kaup，时空分数Fokas方程。分数导数在Caputo的意义上进行了描述。我们获得了上述非线性分数方程的精确解。适当地使用广义分数复变换将这些方程式转换为常微分方程式，随后将其转换为精确解的数量。