In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

中文翻译：

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分数阶导数的时间分数阶复数Ginzburg-Landau方程的新精确行波解

在这项研究中，研究了具有Kerr定律和双幂定律非线性的时间分数复Ginzburg-Landau方程的精确行波解。非线性分数阶微分方程通过一致的分数导数通过行波变换转换为非线性常微分方程。通过利用新的扩展，可以得出一系列解决方案，包括双曲函数解决方案，三角函数解决方案和有理函数解决方案。-扩展方法。通过选择解决方案的适当参数，可以提供数值模拟来进一步解释光脉冲在光纤中的传播。