Periodic and solitary wave solutions to a family of new 3D fractional WBBM equations using the two-variable method

Abstract

For the newly implemented 3D fractional Wazwaz–Benjamin–Bona–Mahony​ (WBBM) equation family, the present study explores exact singular, solitary, and periodic singular wave solutions via the (G′∕G,1∕G)-expansion process. In the sense of conformable derivatives, the equations considered are transformed into ordinary differential equations. In spite of many trigonometric, complex hyperbolic, and rational functions, some fresh exact singular, solitary, and periodic wave solutions to the deliberated equations in fractional systems are attained by the implementation of the (G′∕G,1∕G)-expansion technique through the computational software Mathematica. The unique solutions derived by the process defined are articulated with the arrangement of the functions tanh, sech; tan, sec; coth, csch, and cot, csc. With three-dimensional graphics, some of the latest solutions created have been envisaged, by selecting appropriate arbitrary constraints to illustrate their physical representation. The outcomes which are obtained to show the power of the computational technique for the WBBM equations can be applied to other nonlinear water model equations in ocean and coastal engineering. All the obtained solutions have been verified by the computational software Mathematica.