Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

Abstract

<br />In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He's semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He's semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. Based on this formulation, a solitary solution can be easily obtained using the Ritz method. The Kudryashov method is used to construct exact solutions of the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. Moreover, it is observed that the suggested techniques are compatible with the physical nature of such problems.