<p>Within this study, we delve into the realm of optical solitons under the purview of the fractional complex Ginzburg-Landau equation, integrating influences from the Kerr law, parabolic law, and quadratic cubic law. These solitons reveal many phenomena in the field of physics, spanning secondary phase transformations, non-linear wave dynamics, surface interface interactions, manifestations in superconductivity, implications for field-theory strings, and distinctive behaviours in liquid crystals. Furthermore, our inquiry extends to examining these equations under three distinct operators: conformable, M-truncated, and beta derivatives. Employing a novel mapping technique, we extract various solutions encompassing dark, bright, kink, periodic, periodic singular, singular, and combined dark-bright solitons. Our analysis entails visualising these solutions through 3D and 2D graphs, facilitating comparisons among solutions derived from varying derivative orders. Additionally, we present a comparative analysis of the three operators via 2D graphs, offering insights into their specific effects and behaviours within the study. This endeavour elucidates the characteristics and implications of these differential operators in describing optical solitons within complex nonlinear systems. The novelty of this work lies in the application of a new mapping method to the fractional complex Ginzburg–Landau equation along with a comprehensive comparative analysis of conformable, M-truncated, and beta fractional operators.</p>