This article obtains the optical solitons of the complex fractional Ginzburg–Landau equation by the hypothesis of traveling wave and generalized projective Riccati equation scheme. There are four conditions, Kerr law, parabolic law, power law and dual power law of nonlinearity associated with the model. The constraint conditions for the existence of these solutions have also been discussed. Moreover, the physical significance of the constructed solutions has been provided using graphical representation. A comparative study is made by using two distinct definitions of fractional derivatives namely as Beta and M-truncated. Furthermore, a quantitative overview is also included, which involves solutions to the model under discussion. The complex Ginzburg–Landau equation is subjected to a comprehensive sensitivity analysis. Finally, the modulation instability (MI) analysis of proposed model is also carried out on the basis of linear stability analysis. A dispersion relation is obtained between the wave number and frequency.

本文通过行波假设和广义射影Riccati方程格式得到复分数阶Ginzburg-Landau方程的光孤子。与模型相关的非线性有四个条件，克尔定律、抛物线定律、幂律和对偶幂律。还讨论了这些解存在的约束条件。此外，已使用图形表示提供了所构建解决方案的物理意义。通过使用分数导数的两个不同定义，即 Beta 和 M-截断进行比较研究。此外，还包括定量概述，其中涉及正在讨论的模型的解决方案。复杂的 Ginzburg-Landau 方程经过了全面的敏感性分析。最后，所提出模型的调制不稳定性（MI）分析也是在线性稳定性分析的基础上进行的。获得波数和频率之间的色散关系。