| Summary: | 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.
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