On the Comparison of Perturbation-Iteration Algorithm and Residual Power Series Method to Solve Fractional Zakharov-Kuznetsov Equation

TL;DR

This paper compares two analytical approximation methods, PIA and RSPM, for solving the fractional Zakharov-Kuznetsov equation, demonstrating their effectiveness through examples and comparison with exact solutions.

Contribution

It introduces and compares the perturbation-iteration algorithm and residual power series method for fractional PDEs, highlighting their efficiency and simplicity.

Findings

Both methods produce accurate approximations.

Methods are effective for fractional Zakharov-Kuznetsov equations.

Results are consistent with exact solutions.

Abstract

In this paper, we present analytic-approximate solution of a fractional Zakharov-Kuznetsov equation by means of perturbation-iteration algorithm (PIA) and residual power series method (RSPM). Basic definitions of fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results show that both methods are competitive, effective, convenient and simple to use.