<p>The objective of this article is to give a deep investigation into the dynamics of the conformable time-fractional complex Ginzburg–Landau equation including the Kerr law nonlinearity. Taking advantage of the semi-inverse method, we develop the variational principle, based on which the Hamiltonian is extracted. By means of the Galilean transformation, the governing equation is transformed into a planar dynamical system. Then the bifurcation analysis is presented. Correspondingly, the quasi-periodic and chaotic behaviors of the system are also discussed by introducing three different kinds of the perturbed terms in detail. Finally, two novel methods, the invariant algebraic curve method that is based on the planar dynamical system and the direct mapping method, are used to construct the diverse soliton solutions. A set of the optical solitons like the bright soliton and dark soliton are disclosed. In addition, other wave solutions such as the singular wave, singular periodic wave and algebraic solitary wave solutions are also investigated. The graphic depictions of the solition solutions are presented to elucidate the soliton propagation of the nonlinear optical fiber. It is found that the value of the fractional order <i>v</i> can affect the waveform of the soliton, that is, the smaller its value, the more severe the soliton bending. The findings of this research can make us gain more recognition in the nonlinear dynamic characteristics of the time-fractional complex Ginzburg–Landau equation with the Kerr law nonlinearity and the methods used in this study can be used to explore the other nonlinear partial differential equations in physics.</p>