The (G'/G) - expansion method using modified Riemann-Liouville derivative for some space- time fractional differential equations


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Bekir A., Guner O.

AIN SHAMS ENGINEERING JOURNAL, vol.5, no.3, pp.959-965, 2014 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1016/j.asej.2014.03.006
  • Title of Journal : AIN SHAMS ENGINEERING JOURNAL
  • Page Numbers: pp.959-965

Abstract

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then (G'/G) - expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers' equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation. (C) 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.