A comprehensive study on geometric shape optical soliton solutions to the time-factional nonlinear Schrödinger-Hirota equation

In this study, we investigate the analytical soliton solutions of a fundamental model, namely the nonlinear Schrödinger-Hirota equation, in the context of beta time-fractional derivative. We adopt the (ω′/ω,  1/ω)-expansion method, which is a reliable and straightforward approach to extract fresh and general soliton solutions in terms of hyperbolic, trigonometric, and rational functions. The solitons include anti-kink, anti-bell-shaped, bell-shaped, and periodic solitons. These solitons have significant applications in various scientific fields, such as optical fiber communications, signal processing, plasma physics, and trans-oceanic data transfer. This study demonstrates the significance of fractional-order differentiation in revealing new solitons. We also provide a comprehensive comparison with existing literature in normal and anomalous dispersion regions, highlighting the uniqueness of the solutions. Moreover, the graphical representations are used to illustrate the properties and potential applications of these solitons. This research might contribute to the advancement of nonlinear optical research and technology.