Exact solutions of the nonlinear space-time fractional Schamel equation

Abstract

This study focuses on the nonlinear space-time behavior of a plasma system made up of electrons, positive ions, and negative ions using the fractional Schamel (FS) equation. The main goal is to find exact solutions to the nonlinear FS equation by applying the extended hyperbolic function (EHF) method. The study examines how the fractional order affects the phase velocity, amplitude, and wave width of solitary wave solutions. Different exact solutions were found based on various values of the fractional order. Graphical representations are included to show the physical properties of these solutions. Overall, the results demonstrate that the EHF method is effective and reliable for finding exact solutions to the nonlinear FS equation.