Impact of numerical simulation and fractionality of the 3D fractional WBBM model using GERF and MGERF methods

This study recovers several novel accurate solutions to the 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equation within the framework of numerous nonlinear physical phenomena originating from water wave mechanics. This is accomplished by transforming the WBBM equation into an ordinary differential equation (ODE). The ODE then uses two effective methods based on the conformable derivative: the Generalized Exponential Rational Function (GERF) and Modified Generalized Exponential Rational Function (MGERF) Methods. Periodic solutions, w-shaped solitons, single and multiple solitons, dark-bright, and Jacobi elliptic doubly periodic type solutions are thus explored. Applications of the GERF and MGERF approach in many scientific and technical domains assist in expanding our understanding of nonlinear systems, establishing mathematical methodologies, and supporting research solutions. The Modified Variational Iteration (MVI) method, a numerical technique, is employed to derive the approximate solutions to the WBBM problem. An analysis is conducted between this inquiry's findings and those previously acquired through different approaches. All produced wave solutions are determined to be novel in the sense of applied technique, fractionality, and unconstrained parameters. The consequences of unconstrained parameters and fractionality on the resulting solutions are explained physically and shown in a figure. When fractionality and the number of unbound parameters rise, the wave portents shift. Finally, this article dynamically demonstrates that appropriate transformation and relevant GERF and MGERF techniques are more helpful in studying the dynamics of water waves and might be used in future research to clarify other physical phenomena.