On the analytical solutions of conformable time-fractional extended Zakharov–Kuznetsov equation through ( $$G'/G^{2}$$ G ′ / G 2 )-expansion method and the modified Kudryashov method

Abstract

The aim of this article is to obtain and study the solutions of conformable time fractional (1+2)-dimensional extended Zakharov–Kuznetsov equation (2D-FZKE) which is modeled to investigate the waves in magnetized plasma. Wave transformation in fractional form is applied to convert the original fractional order nonlinear partial differential equation into another nonlinear ordinary differential equation. The strategy here consists of using ( $$G'/G^{2}$$ )-expansion method and the modified Kudryashov method to obtain a variety of exact solutions. Both schemes work well and reveal distinct exact solutions. These solutions are of significant importance in plasma physics where the 2D-FZKE is modeled for some special physical phenomenon.