Exact and explicit travelling-wave solutions to the family of new 3D fractional WBBM equations in mathematical physics

In this paper, the new 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations newly announced are investigated with the introduction of the spatial and sequential fractional-order derivatives expending in the sense of conformable derivative. Several solutions containing hyperbolic and trigonometric function solutions are created using the modified extended tanh-function (mETF) method. The productivity of the mETF process for building these solutions has been established. This method decreases the large volume of calculations. With the assist of computational software MALAB, the solutions' graphical exemplifications are illustrated in three-dimension (3D) and two-dimension (2D) plot. All plots represent the absolute wave configurations through the obtained solutions to the mentioned equation, preferring suitable parameters. Moreover, it may conclude that the attained solutions and their physical features might help comprehend the shallow water wave propagation in nonlinear dynamics.