Investigation of new analytical and numerical solutions of the extended (2+1) dimensional Boussinesq equation using fractional derivative approaches

This study investigates the new fractional (2+1)-dimensional, extended Boussinesq (eBO) equation, which models the behavior of shallow water waves in channels with constant depth and flow velocity. This equation holds considerable relevance in fields such as ocean engineering, coastal hydrodynamics, plasma physics, and nonlinear wave theory. By applying the (m+1/G ')-expansion method, the sub-equation method, and dummyTXdummy-the modified extended tanh function method within the framework of conformable derivatives, a wide array of analytical traveling wave solutions is obtained. These include dark, bright, periodic, singular, exponential, and generalized hyperbolic-type solitons with kink-like features. The fractional transformation technique transforms the original fractional partial differential equations into ordinary differential equations, thereby simplifying the solution process. Moreover, the residual power series method (RPSM) is employed to approximate the solution of this equation, and modulation instability (MI) analysis is conducted to evaluate the stability of the obtained analytical solutions. The study includes comparison tables and various graphical representations to validate the solutions. The numerical findings demonstrate that all methods effectively provide exact and approximate solutions to nonlinear fractional differential equations. The temporal progression and spatial features of the solutions are visualized through 2D, 3D, and contour plots with a comparison of different fractional values. Computational validations are conducted using software, demonstrating the efficiency and general applicability of the proposed approach.

Journal

JOURNAL OF COMPUTATIONAL PHYSICS

Year

2026

Volume

551

ISSN

0021-9991

eISSN

1090-2716

DOI

10.1016/j.jcp.2026.114654

WoS UID

WOS:001672641300001