Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(11): 110204    DOI: 10.1088/1674-1056/21/11/110204
GENERAL Prev   Next  

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
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.
Keywords:  fractional calculus      complex transformation      modified Riemann-Liouville derivative      improved (G'/G)-expansion function method  
Received:  11 February 2012      Revised:  17 May 2012      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
Corresponding Authors:  Khaled A. Gepreel     E-mail:  kagepreel@yahoo.com

Cite this article: 

Khaled A. Gepreel, Saleh Omran Exact solutions for nonlinear partial fractional differential equations 2012 Chin. Phys. B 21 110204

[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
[1] Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control
Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Chin. Phys. B, 2020, 29(5): 050504.
[2] Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order
Qiu-Yan He(何秋燕), Bo Yu(余波), Xiao Yuan(袁晓). Chin. Phys. B, 2017, 26(4): 040202.
[3] A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations
Li-Min Zhang(张立民), Ke-Hui Sun(孙克辉), Wen-Hao Liu(刘文浩), Shao-Bo He(贺少波). Chin. Phys. B, 2017, 26(10): 100504.
[4] New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods
S Saha Ray. Chin. Phys. B, 2016, 25(4): 040204.
[5] Abundant solutions of Wick-type stochastic fractional 2D KdV equations
Hossam A. Ghany, Abd-Allah Hyder. Chin. Phys. B, 2014, 23(6): 060503.
[6] The fractional coupled KdV equations:Exact solutions and white noise functional approach
Hossam A. Ghany, A. S. Okb El Bab, A. M. Zabel, Abd-Allah Hyder. Chin. Phys. B, 2013, 22(8): 080501.
[7] Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative
Rajneesh Kumar, Vandana Gupta. Chin. Phys. B, 2013, 22(7): 074601.
[8] Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus
Wang Fa-Qiang, Ma Xi-Kui. Chin. Phys. B, 2013, 22(3): 030506.
[9] A new generalized fractional Dirac soliton hierarchy and its fractional Hamiltonian structure
Wei Han-Yu, Xia Tie-Cheng. Chin. Phys. B, 2012, 21(11): 110203.
[10] Chaos in a fractional-order micro-electro-mechanical resonator and its suppression
Mohammad Pourmahmood Aghababa. Chin. Phys. B, 2012, 21(10): 100505.
[11] A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system
Si Gang-Quan, Sun Zhi-Yong, Zhang Yan-Bin. Chin. Phys. B, 2011, 20(8): 080505.
[12] Synchronization in a unified fractional-order chaotic system
Wu Zheng-Mao, Xie Jian-Ying. Chin. Phys. B, 2007, 16(7): 1901-1907.
[13] Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization
Lu Jun-Guo. Chin. Phys. B, 2006, 15(2): 301-305.
[14] Chaotic dynamics and synchronization of fractional-order Genesio--Tesi systems
Lu Jun-Guo. Chin. Phys. B, 2005, 14(8): 1517-1521.
No Suggested Reading articles found!