Optical soliton analysis to a family of 3D WBBM equations with conformable derivative via a dynamical approach

The prime goal of this study is to investigate the soliton dynamics to the family of 3D fractional Wazwaz–Benjamin–Bona–Mahony​ (WBBM) equations in the absence of self-phase modulation by employing the advanced exp−ϕψ-expansion method. Our mentioned technique is a superior development of the generalized exp−ϕψ-expansion method. By employing the advanced exp−ϕψ-expansion method, optical soliton, singular optical soliton, dark optical soliton, combined optical soliton solutions are constructed to our mentioned family of 3D fractional WBBM equations, whereas trigonometric, hyperbolic, and rational function solutions are also obtained. Moreover, three-dimensional surface plots, contour plots, and two-dimensional plots are presented by the obtained solutions’ dynamical characteristics. All the plots of each solution are shown separately for real and imaginary parts. All the attained solutions have been proved by the computational software Mathematica.