The (G '/G,1/G)-expansion method for solving nonlinear space-time fractional differential equations


YAŞAR E., Giresunlu I. B.

PRAMANA-JOURNAL OF PHYSICS, vol.87, no.2, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s12043-016-1225-7
  • Journal Name: PRAMANA-JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Exact solution, modified Riemann-Liouville fractional derivative, space-time Cahn-Allen equation, space-time Klein-Gordon equation, (G '/G,1/G)-expansion method, COMPLEX TRANSFORM
  • Bursa Uludag University Affiliated: Yes

Abstract

In this work, we present (G'/G,1/G)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space-time fractional Cahn-Allen equation and space-time fractional Klein-Gordon equation. The fractional derivatives are described in the sense of modified Riemann-Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems. The (G'/G,1/G)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.