On the solitonic structures for the fractional Schrödinger–Hirota equation

In this article, the fractional Schrödinger–Hirota equation which is a generalization of the standard Schrödinger equation which, in particular, explain how soliton transmission behaves on fiber optic systems in physics when data is transmitted over long distances with a wide bandwidth. A collection of comprehensive soliton structures are developed to study the behaviour of the governing model with the aid of some efficient explicit strategies namely the \(\exp (-\psi (\zeta ))\) $exp(-\psi (\zeta ))$ -expansion method and the Sardar sub-equation method. By transforming the original equation into a system of ordinary differential equations, it becomes possible to obtain explicit solutions with a high degree of accuracy. These solutions incorporate dark soliton and trigonometric function solutions, dark singular solition plane wave, singular solition, opposite singular solition, smooth, bell shaped, w-shaped periodic, bright, anti kink, singular bell shaped solitons and traveling wave structures.