Applications of fractional complex transform and $left( frac{G^{prime }}{G}right) $-expansion method for time-fractional differential equations |
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| Authors: | Ahmet Bekir Ozkan Guner Omer Unsal Mohammad Mirzazadeh |
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| Affiliation: | Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir-TURKEY,Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri-TURKEY,Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir-TURKEY and Guilan University, Mathematical Science Faculty, Department of Mathematics, Rasht-IRAN |
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| 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 expressedin 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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| Keywords: | The $left( frac{G^{prime }}{G}right) $-expansion method exact solutions, fractional differential equation modifiedRiemann--Liouville derivative. |
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