Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves

Abstract This article investigates fluid flow in a dynamic system using the coupled Boussinesq–Burgers equation to precisely narrate the propagation of shallow water waves. This work proposes a novel approach to using the quintic B-spline technique to obtain an approximate solution to the nonlinear fractional coupled Boussinesq–Burgers equation. For discretizing time, the Caputo fractional derivative is used to handle the fractional derivative effectively, while the quintic B-spline function is used to interpolate the spatial derivative. We provide two numerical examples to show the level of accuracy and practicality of the current scheme in solving the fractional coupled Boussinesq–Burgers problem and see how observe the effect of the fractional-order on wave propagation. In addition, we conduct a stability analyzis and numerically determine the order of convergence. We compute the error norms to assess the accuracy of the proposed method.