Traveling Wave Solutions of Fractional Differential Equations Arising in Warm Plasma

Abstract

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

Keywords

• Caputo fractional derivative, Fractional Adomian decomposition method, Fractional Kawahara equation, Fractional Korteweg–De Vries equation, Riemann–Liouville fractional integral