Propagation of M-truncated optical pulses in nonlinear optics

This article discusses the Hamiltonian amplitude equation with the properties of truncated M-fractional derivative. The proposed equation governs certain instabilities of modulated wave trains. The optical pulses in different forms like, bright, dark, singular, combined and complex solitons are extracted by using the modified Sardar sub-equation method, a relatively new integration tool. Moreover, hyperbolic, exponential, and periodic solutions are guaranteed. The applied technique provides earlier extracted results and also reveals new solutions as well as useful for explaining nonlinear partial differential equations. Three dimensional, two dimensional, contour, and density profiles are plotted with the correct parameter values, and communicate about the physical representation of some solutions. Our extracted results are found to be novel in the study as they are compared to previously published research. This study will be valuable to a variety of engineers who specialise in engineering models. In our opinion, the results demonstrate that the computational method utilised is effective, straightforward, and applicable even to complicated systems.