| Volume 6, Number 1, 2016, Pages 131-144 DOI：10.11948/2016011 |
| Applications of fractional complex transform and $\left( \frac{G^{\prime }}{G}\right) $-expansion method for time-fractional differential equations |
| Ahmet Bekir,Ozkan Guner,Omer Unsal,Mohammad Mirzazadeh |
| Keywords:The $\left( \frac{G^{\prime }}{G}\right) $-expansion method exact solutions, fractional differential equation modifiedRiemann--Liouville derivative. |
| Abstract: |
| In this paper, the fractional complex transform and the $\left( \frac{G^{\prime }}{G}\right) $-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. |
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