This paper investigates the optical solitons to the M-truncated fractional (1+1)-dimensional nonlinear generalized Bretherton model with arbitrary constants. It is employed to forecast the movement of liquid droplets or gas bubbles in microchannels, which is crucial for drug delivery systems, biomedical diagnostics, and lab-on-a-chip technologies. We obtain optical soliton solutions using the extended hyperbolic function method (EHFM) and the modified extended tanh method (METM). Numerous solutions, such as singular, periodic–singular, bright, and dark optical solitons, are obtained from our investigation. The 2D graphical depiction of the solutions shows a variety of wave patterns that change with varied values of α and t. The wave’s amplitude forms become more apparent as α and t increase. Using 2D plots, the comparison of fractional effects for the M-truncated fractional derivative is demonstrated by giving specific values to the fractional parameter.
Khushi et al. (Sat,) studied this question.