The extended complex method is investigated for exact analytical solutions of nonlinear fractional Liouville equation. Based on the work of Yuan et al., the new rational, periodic, and elliptic function solutions have been obtained. By adjusting the arbitrary values to the constants in the constructed solutions, it can describe the physical phenomena to the traveling wave solutions, since traveling wave has significant value in applied sciences and engineering. Our results indicate that the extended complex technique is direct and easily applicable to solve the nonlinear fractional partial differential equations (NLFPDEs).

中文翻译：

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非线性分数阶Liouville方程的精确解析解的扩展复方法

研究了扩展复数法，以求解非线性分数阶Liouville方程的精确解析解。根据Yuan等人的工作，获得了新的有理，周期和椭圆函数解。由于行波在应用科学和工程中具有重要的价值，因此通过将所构造的解中的任意值调整为常数，可以描述行波解的物理现象。我们的结果表明，扩展复杂技术可以直接轻松地用于求解非线性分数阶偏微分方程（NLFPDE）。