APPLICATIONS OF FRACTIONAL COMPLEX TRANSFORM AND (G '/G)-EXPANSION METHOD FOR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS

Bekir A., GÜNER Ö., ÜNSAL Ö., Mirzazadeh M.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, vol.6, no.1, pp.131-144, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 1
  • Publication Date: 2016
  • Journal Name: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.131-144
  • Keywords: The (G '/G)-expansion method, exact solutions, fractional differential equation, modified Riemann-Liouville derivative, FITZHUGH-NAGUMO EQUATION, NONLINEAR EVOLUTION-EQUATIONS, TRAVELING-WAVE SOLUTIONS, MODIFIED KDV EQUATION, VARIABLE-COEFFICIENTS, MATHEMATICAL PHYSICS, MKDV EQUATION, EXPLICIT, CALCULUS
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this paper, the fractional complex transform and the (G '/G)-expansion method are employed to solve the time-fractional modfied Korteweg-de Vries equation (fmKdV), Sharma-Tasso-Olver, Fitzhugh-Nagumo equations, where G satisfies a second order linear ordinary differential equation. Exact solutions are expressed in terms of hyperbolic, trigonometric and rational functions. These solutions may be useful and desirable to explain some nonlinear physical phenomena in genuinely nonlinear fractional calculus.