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

Abstract

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.