International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

The first integral method and its application for finding the exact solutions of nonlinear fractional partial differential equations (PDES) in the mathematical physics

Elsayed M. E. Zayed
  • Elsayed M. E. Zayed
  • Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt.
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Yasser A. Amer
  • Yasser A. Amer
  • Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt.
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  •  Received: 11 February 2014
  •  Accepted: 21 March 2014
  •  Published: 30 April 2014

Abstract

In this article we apply the first integral method to construct the exact solutions of some nonlinear fractional partial differential equations (PDES) in the sense of modified Riemann–Liouville derivatives, namely the nonlinear fractional Zoomeron equation and the nonlinear fractional Klein- Gordon- Zakharov system of equations. Based on a nonlinear fractional complex transformation, these two nonlinear fractional equations can be turned into nonlinear ordinary differential equations (ODE) of integer order. This method has more advantages: it is direct and concise.

Key words: First integral method, exact solutions, nonlinear fractional Zoomeron equation, nonlinear fractional Klein-Gordon-Zakharov system of equations.