Analyzing fractional effects on solutions of the generalized perturbed Zakharov-Kuznetsov equation using a residual series method with Caputo derivatives

In this article, we discuss an analytical method to solve physical equations occurring in acoustic waves. We acquire an approximate solution to the generalized fractional perturbed Zakharov-Kuznetsov (ZK) equation via the Residual power series method (RPSM). Three problems are considered to demonstrate the validity, efficiency and accuracy of the proposed method. The RPSM solution agrees very well with the results those obtained by q-homotopy perturbation transform method (q-HPTM) and the exact solution. The final results are shown through 3D graphs, 2D graphs and numerical tables. The results demonstrate the quality and power of the presented method. Fractional derivatives in the manuscript are defined in the Caputo's sense whose order varies from 0 to 1. For mathematical computation Mathematica 10 is used.