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Chin. Phys. B, 2013, Vol. 22(11): 110202    DOI: 10.1088/1674-1056/22/11/110202
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Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

Ahmet Bekira, Özkan Günerb
a Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey;
b Dumlupínar University, School of Applied Sciences, Department of Management Information Systems, Kutahya, Turkey
Abstract  In this paper, we use the fractional complex transform and the (G’/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie’s modified Riemann–Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.
Keywords:  (G’/G)-expansion method      time-fractional Burgers equation      fractional-order biological population model      space–time fractional Whitham–Broer–Kaup equations  
Received:  04 March 2013      Revised:  04 April 2013      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.70.Wz (Symbolic computation (computer algebra))  
  05.45.Yv (Solitons)  
  94.05.Fg (Solitons and solitary waves)  
Corresponding Authors:  Ahmet Bekir     E-mail:  abekir@ogu.edu.tr

Cite this article: 

Ahmet Bekir, Özkan Güner Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method 2013 Chin. Phys. B 22 110202

[1] Miller K S and Ross B 1993 An Introduction to the Fractional Calculus and Fractional Differential Equations (New York: Wiley)
[2] Podlubny I 1999 Fractional Differential Equations (California: Academic Press)
[3] Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
[4] Zhang S and Zhang H Q 2011 Phys. Lett. A 375 1069
[5] Tong B, He Y, Wei L and Zhang X 2012 Phys. Lett. A 376 2588
[6] Guo S, Mei L, Li Y and Sun Y 2012 Phys. Lett. A 376 407
[7] Lu B 2012 J. Math. Anal. Appl. 395 684
[8] Zheng B 2012 Commun. Theor. Phys. 58 623
[9] Gepreel K A and Omran S 2012 Chin. Phys. B 21 110204
[10] Wang M, Li X and Zhang J 2008 Phys. Lett. A 372 417
[11] Zhang S, Tong J L and Wang W 2008 Phys. Lett. A 372 2254
[12] Bekir A 2008 Phys. Lett. A 372 3400
[13] Zayed E M E and Gepreel K A 2009 J. Math. Phys. 50 013502
[14] Jumarie G 2006 Comput. Math. Appl. 51 1367
[15] Jumarie G 2009 Appl. Maths. Lett. 22 378
[16] Li Z B and He J H 2010 Math. Comput. Appl. 15 970
[17] Li Z B and He J H 2011 Nonlinear Sci. Lett. A Math. Phys. Mech. 2 121
[18] Inc M 2008 J. Math. Anal. Appl. 345 476
[19] El-Sayed A M A, Rida S Z and Arafa A A M 2009 Commun. Theor. Phys. 52 992
[20] Lu B 2012 Phys. Lett. A 376 2045
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