Soliton solutions of fractional complex Ginzburg-Landau equation with Kerr law and non-Kerr law media

In this study, new soliton solutions of the fractional complex Ginzburg-Landau equation, that models soliton propagation in the presence of detuning factor, have been constructed. The Kerr law, power law, dual-power law and log law nonlinearity have been considered. The exp(−ϕ(ξ))-expansion method has been utilized for finding new exact solutions of fractional complex Ginzburg-Landau equation. Different forms of solutions, including the hyperbolic, trigonometric and rational function solutions are formally extracted. The method suggests a useful and efficient technique to look for the exact solutions of a wide range of nonlinear fractional partial differential equations.