In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.
Construction of modulation instability analysis and optical soliton solutions of pertubed nonlinear Schrödinger dynamical equation with power law nonlinearity in non-kerr medium