New optical solitons for complex Ginzburg–Landau equation with beta derivatives via two integration algorithms

This paper explores the optical solitons with Kerr laws nonlinearity for the complex Ginzburg–Landau equation with M-truncated and beta derivatives which describes solitons propagation. In this regard, two new methods, namely extended sub-equation and unified solver method, are used. From general, hyperbolic, and trigonometric functions, we obtain novel and general solitary solutions. All obtained solutions can be useful for a variety of important experiments in nuclear physics, fluid mechanics, and particle physics. Our results show the strength of the proposed technique for the determination of optical solitons of nonlinear evolution equations. The proposed methods can be applied for solving other fractional space–time NLEs arising in nonlinear optics.