An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense

The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

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The paper presents a systematic study on a time-fractional nonlinear water wave equation using a new analytical method, providing approximate solutions and analyzing the influence of the Caputo operator on the solutions. Graphical illustrations and numerical tables are used to support the effectiveness of the new analytical method in handling the water wave equation.