Numerical solution of time fractional Korteweg-de Vries-Burgers equation in a dusty plasma with non-extensive distributed electrons

Abstract

In this article, the Korteweg-de Vries-Burgers equation (KdVBE) is derived for ion-acoustic shocks in a dusty plasma considering warm ions, electrons and dust. The set of equations is normalized using different schemes, and the reductive perturbation technique (RPT) is applied to derive the model. The KdVBE is converted to time fractional KdVBE and then numerical scheme is formulated for the solution of time fractional KdVBE. A radial basis function collocation scheme and the Crank-Nicolson scheme are applied on time fractional KdVBE. The time-fractional derivative is discretized using the Caputo-Fabrizio fractional derivative. Moreover, a theta-weighted scheme is implemented for the spatial derivatives, in which radial basis functions are used for space derivatives in which radial basis function is used to approximate the derivatives. The behaviour of the method is assessed with the help of graphs and tables, and also shows the effect of the Caputo-Fabrizio fractional derivative. Numerical simulations indicate that the proposed scheme is highly efficient to find more accurate results. The solution is obtained for a variety of parameters to describe their behaviour of parameters like temperature ratio, fractional parameter and non-extensive distribution. The accuracy of the proposed method is verified by comparing the results with other methods in the literature.