Abstract
The fractional complex Ginzburg–Landau equation plays an important role in the field of optics, field theory and superconductivity. In this paper, two variable G′G,1G–expansion method has been used on the fractional complex Ginzburg–Landau equation. The governing model is studied with three kinds of nonlinearities, namely; Kerr, quadratic–cubic and parabolic laws. Each law applied on fractional complex Ginzburg–Landau model is further discussed along with three definitions of the derivative i.e., beta derivative, conformable derivative and M-truncated derivative. In order to observe the fractional effects, a graphical comparison is shown. The evolution of solutions of the governing model for increasing value of fractional parameter is depicted through the surface graphs and line plots.
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