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

Ahmet Bekir; Ozkan Guner; Ömer Ünsal; Mohammad Mirzazadeh

doi:10.11948/2016011

2016 Volume 6 Issue 1

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Ahmet Bekir, Ozkan Guner, Ömer Ünsal, Mohammad Mirzazadeh. APPLICATIONS OF FRACTIONAL COMPLEX TRANSFORM AND (G'/G)-EXPANSION METHOD FOR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 131-144. doi: 10.11948/2016011

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Ahmet Bekir, Ozkan Guner, Ömer Ünsal, Mohammad Mirzazadeh. APPLICATIONS OF FRACTIONAL COMPLEX TRANSFORM AND (G'/G)-EXPANSION METHOD FOR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 131-144. doi: 10.11948/2016011

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

1 Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir-TURKEY;
2 Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri-TURKEY;
3 Guilan University, Mathematical Science Faculty, Department of Mathematics, Rasht-IRAN

Abstract

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.
- The(G'/G)-expansion method /
- exact solutions /
- fractional differential equation /
- modified Riemann-Liouville derivative
MSC: 34A08;35R11;37H10;26A33;35Q68

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References

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