Some exact solutions of the nonlinear space–time fractional differential equations

Abstract

ABSTRACTIn this article, we construct exact soliton solutions of the nonlinear space–time fractional Klein–Gordon equation, Hirota–Satsuma coupled KdV (HSC KdV) system, coupled Whitham–Broer–Kaup (WBK) system, and KdV–Zakharov–Kuznetsov (KdV-ZK) equation using exponential rational function method. Our solutions include soliton-like, singular soliton, and kink solutions. Two-dimensional and three-dimensional graphical representation of all solutions is also presented to understand the accuracy of the technique. Moreover, a comparison of the recent solutions is made with some already existing solutions. It has been shown that the suggested method will be helpful in finding the solutions of different kind of nonlinear fractional differential equations emerging in mathematical physics. Throughout the paper, all the calculations are made with the aid of the Maple software.