In the present work, the optical soliton solutions to the 2-dimensional fractional coupled nonlinear Schrödinger model with \(\mathfrak {B}\) eta fractional derivative are found using the unified Riccati equation expansion ( \(\textrm{UREE}\) ) approach. These solutions are essential to understand wave propagation in a range of physical domains. In real-world applications where precise wave motion is crucial, such as control systems, signal processing, and fiber optic networks, these models are crucial. We successfully employ the \(\textrm{UREE}\) approach and secure some novel optical solutions in the shape of singular, dark periodic and rational wave solutions. Additionally, to explore the fact that the model is highly sensitive, we discussed the time series and sensitivity analysis of the examined model. The investigations, which concentrate on the nonlinear dynamic behaviors of the solutions, are new and unexplored. These behaviors are shown in 3-D plots, contour plots and 2-D curves and descriptions of the related physical properties. Our results show that the use of the \(\textrm{UREE}\) approach for producing optical solutions and looking at them in fractional nonlinear models and dynamical data offers useful mathematical tools in applied mathematics and the investigation of wave motion in shallow water.
