Dispersive optical soliton solutions to the truncated time M-fractional paraxial wave equation with its stability analysis

This article investigates the truncated time M-fractional paraxial wave equation. This model is frequently used to depict the activation of waves in utterly different physical frameworks, such as quantum mechanics and optics. Two trustworthy methodologies, the improved F-expansion and modified exponent function method, are used to obtain the different soliton solutions to the truncated time M-fractional paraxial wave equation. The obtained solutions offer a valuable understanding of the underlying physical events. Discussion is also had over the equation’s modulation instability, which confirms the given equation is stable. Several graphical charts, including 2D, 3D, density, and contour, are produced using symbolic software. These visual representations have a significant positive impact on qualitative evaluations of diverse natural occurrences. The evaluated findings showed that the approaches employed in this work to obtain inclusive and standard solutions are efficient and speedier in computing, they will be beneficial in addressing more difficult higher order nonlinear perturbed truncated time M-fractional models.