Numerical solution of nonlinear fractional Zakharov–Kuznetsov equation arising in ion-acoustic waves

Abstract

The main purpose of this work is to suggest an efficient hybrid computational technique, namely the q-homotopy analysis transform method (q-HATM) to find the solution of the nonlinear time-fractional Zakharov–Kuznetsov (FZK) equation in two dimensions. The uniqueness and convergence analysis of the nonlinear time-FZK equation is presented. The Laplace decomposition method (LDM) is also employed to get the approximate solution of the nonlinear FZK equation. We implemented these techniques on two numerical examples, plotted the solution and compared the absolute error with the variational iteration technique and homotopy perturbation transform technique to show the efficiency of these techniques.