<p>This paper applies the simplest equation method to examine the dual-mode nonlinear conformable Schrödinger equation incorporating quadratic–cubic nonlinearity. A variety of novel optical soliton solutions are obtained, encompassing kink-shaped, dark–bright mixed, multi-bright, dark, and wave-like soliton profiles. These solutions are visualized through contour plots, as well as two-dimensional and three-dimensional graphical simulations. Furthermore, the influence of the conformable derivative parameter and temporal parameter on the optical solitons is analyzed, emphasizing their crucial roles in shaping soliton properties. A key contribution of this study is the in depth analysis of fractional-order dynamics introduced through the conformable derivative, which uncovers new possibilities for controlling soliton properties such as velocity, phase, and spatial localization. This approach enhances the understanding of how nonlinearity, dispersion, and fractional-order effects interact, providing a foundation for novel techniques in optical pulse shaping and photonic system design. The results hold promising implications for the advancement of optical communication technologies, where stable solitonic waveforms are essential for reliable information transmission through nonlinear media.</p>