Dynamical perspective of sensitivity analysis and optical soliton solutions to the fractional Benjamin–Ono model

In the current research, one of the most prevalent models of oceanic engineering is examined for its analytical and approximate analysis. With the application of a robust analytical strategy, the extended and modified Tanh-Function methodology, we examined the fractional Benjamin–Ono (BO) equation. The technique mentioned has an abundance of success with deep-water internal waves. Identifying precise solitary pulse solutions to nonlinear partial differential equations with fractional parameters in this manner is efficient as well as productive. Using such a novel strategy, we investigate the fractional BO equation for the first time and produce some distinctive analytical findings. Also, explore its sensitivity analysis to identify that the model is highly sensitive. The innovative, isolated, and precise approximation solutions of the considered model have been extracted using an analytical approach. •Fractional Benjamin–Ono (BO) equation of oceanic engineering.•Extended and modified tanh-function methodology.•Sensitivity analysis is studied effectively.•Geometric visualizations of diverse soliton and exact solutions are displayed to give more physical perspective.•Numerical visualization showcases intricate solutions.