Enabling technologies in optical and plasma engineering through fractional soliton dynamics

In this study, we explore the third-order fractional nonlinear Schrödinger equation in the context of the M-truncated fractional derivative, a model of key significance to nonlinear optics and plasma physics. Through the use of the generalized Riccati equation mapping technique and undetermined coefficient technique, we obtain a wide range of soliton solutions, such as bright, dark, bright–dark, dark-singular and periodic-singular optical solitons. These wave patterns play important roles in characterizing self-trapped optical beams in nonlinear media, pulse propagation in optical fibers, and localized excitations in plasma systems. For validation and numerical comparison, the differential transform method is used, yielding approximate solutions corresponding to the analytical forms. The implications of varying the fractional order are revealed using 3-dimensional, 2-dimensional, and density plots, showing how fractional dynamics affect dispersion control, pulse stability and nonlinear interaction features. The findings show how fractional order models can be used to improve optical communication system design, manipulate energy localization in plasmas, and enhance nonlinear wave propagation in new photonic and plasma technologies.