On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water

In the present article, Petrov–Galerkin method has been utilized for the numerical solution of nonlinear time-fractional KdV–Burgers (KdVB) equation. The nonlinear KdV–Burgers equation has been solved numerically through the Petrov–Galerkin approach utilising a quintic B-spline function as the trial function and a linear hat function as the test function . The numerical outcomes are observed in good agreement with exact solutions for classical order. In case of fractional order, the numerical results of KdV–Burgers equations are compared with those obtained by new method proposed in [1] . Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear dispersive and dissipative problems like the time-fractional KdV–Burgers equation.