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Exact solutions for nonlinear partial fractional differential equations |
Khaled A. Gepreela b, Saleh Omranb c |
a Mathematics Department, Faculty of Science, Zagazig University, Egypt; b Mathematics Department, Faculty of Science, Taif University, Saudi Arabia; c Mathematics Department, Faculty of science, South Valley University, Egypt |
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Abstract In this article, we use the fractional complex transformation to convert the nonlinear partial fractional differential equations to the nonlinear ordinary differential equations. We use the improved (G'/G)-expansion function method to calculate the exact solutions for the time and space fractional derivatives Foam Drainage equation and the time and space fractional derivatives nonlinear KdV equation. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.
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Received: 11 February 2012
Revised: 17 May 2012
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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Corresponding Authors:
Khaled A. Gepreel
E-mail: kagepreel@yahoo.com
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Cite this article:
Khaled A. Gepreel, Saleh Omran Exact solutions for nonlinear partial fractional differential equations 2012 Chin. Phys. B 21 110204
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[1] |
Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press)
|
[2] |
He J H 2004 Bull. Sci. Technol. 15 86
|
[3] |
Diethelm K and LuchkoY 2008 J. Comput. Anal. Appl. 6 243
|
[4] |
Erturk V S, Momani S and Odibat Z 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 1642
|
[5] |
Daftardar-Gejji V and Bhalekar S 2008 Appl. Math. Comput. 202 113
|
[6] |
Daftardar-Gejji V and Jafari H 2007 Appl. Math. Comput. 189 541
|
[7] |
Sweilam N H, Khader M M and Al-Bar R F 2007 Phys. Lett. A 371 26
|
[8] |
Golbabai A and Sayevand K 2011 Comput. Math. Application 61 2227
|
[9] |
Golbabai A and Sayevand K 2010 Nonlinear Science Lett. A 1 147
|
[10] |
Gepreel K A 2011 Applied Math. Lett. 24 1428
|
[11] |
Deng W H 2010 Nonlinear Analysis: TMA 72 1768
|
[12] |
Deng W H 2007 Journal of Computational Physics 227 1510
|
[13] |
Wang M L, Li X Z and Zhang J L 2008 Phys. Lett. A 372 417
|
[14] |
Zayed E M E and Gepreel K A 2009 J. Math. Phys. 50 013502
|
[15] |
Zhang H 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3220
|
[16] |
Dahmani Z and Anber A 2010 Inter. J. Nonlinear Sci. 10 39
|
[17] |
Momani S, Odibat Z and Alawneh A 2008 J. Numer. Method. Partial Diff. Equ. 24 262
|
[18] |
Kolwankar K M and Gangal A D 1998 Phys. Rev. Lett. 80 214
|
[19] |
Chen W and Sun H G 2009 Mod. Phys. Lett. B 23 449
|
[20] |
Cresson J 2005 J. Math. Anal. Appl. 307 48
|
[21] |
Jumarie G 2006 Comput. Math. Appl. 51 1367
|
[22] |
Jumarie G 2006 Appl. Math. Lett. 19 873
|
[23] |
Wu G C 2011 Appl. Math. Lett. 24 1046
|
[24] |
Jumarie G 2006 Math. Comput. Modelling 44 231
|
[25] |
Jumarie G 2009 Appl. Math. Lett. 22 1659
|
[26] |
Almeida R, Malinowska A B and Torres D FM 2010 J. Math. Phys. 51 033503
|
[27] |
Wu G C and Lee E W M 2010 Phys. Lett. A 374 2506
|
[28] |
Malinowska A B, Sidi Ammi M R and Torres D F M 2010 Commun. Frac. Calc. 1 32
|
[29] |
Wu G C 2010 Commun. Frac. Calc. 1 23
|
[30] |
Li Z B and He J H 2010 Math. Comput. Applications 15 970
|
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