# Analytical treatment of the fractional Zakharov–Kuznetsov equation via the generalized integral residual power series method

## TL;DR

This paper introduces a new method for solving a complex equation used to model plasma waves, showing it is accurate and reliable.

## Contribution

A novel generalized integral residual power series method is proposed for solving nonlinear fractional differential equations.

## Key findings

- GIRPSM improves accuracy and convergence for solving the fractional Zakharov–Kuznetsov equation.
- The method is effective for nonlinear fractional partial differential equations in plasma wave modeling.
- Numerical results confirm the robustness and reliability of the proposed method.

## Abstract

This study presents a generalized integral residual power series method (GIRPSM) for finding semi-analytical solutions to the nonlinear fractional Zakharov–Kuznetsov equation (FZKE). This method combines the residual power series method with a new general integral transform to improve accuracy and convergence. The effectiveness of this method is demonstrated by the robustness of the numerical results. The results demonstrate that GIRPSM is highly accurate and reliable in solving nonlinear fractional partial differential equations, including those modeling plasma wave propagation.