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He’s semi-inverse method; ansatz method; nonlinear fractional Klein–Gordon equation; generalized Hirota–Satsuma coupled KdV system.

This paper investigates, for the first time, the applicability and effectiveness of He’s semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He’s semi-inverse variational principle method and the ansatz method are used to construct exact solutions of nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.

M Mirzazadeh¹

1. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran

Published

July 2015

Manuscript received

11 April 2014

Manuscript revised

30 May 2014

Accepted

11 June 2014

Early published

29 November 2014