Variational iteration method for solving the time-fractional diffusion equations in porous medium

doi:10.1088/1674-1056/21/12/120504

Abstract The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.

Keywords: time-fractional diffusion equation Captuo derivative Riemann-Liouville derivative variational iteration method Laplace transformation

Received: 28 June 2012
Revised: 28 July 2012
Accepted manuscript online:

PACS:	05.45.Df	(Fractals)
	45.10.Hj	(Perturbation and fractional calculus methods)
	66.30.Pa	(Diffusion in nanoscale solids)
	45.10.Db	(Variational and optimization methods)

Fund: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 51134018).

Corresponding Authors: Wu Guo-Cheng
E-mail: wuguocheng2002@yahoo.com.cn

Cite this article:

Wu Guo-Cheng (吴国成) Variational iteration method for solving the time-fractional diffusion equations in porous medium 2012 Chin. Phys. B 21 120504

[1]	Santos M C, Lenzi E, Gomes E M, Lenzi M K and Lenzi E K 2011 Int. Rev. Chem. Eng. 3 814
[2]	Fujioka J 2011 Commun. Frac. Calc. 1 1
[3]	Hristov J 2011 Int. Rev. Chem. Eng. 3 814
[4]	Chen W and Holm S 2004 J. Acoustic Soc. Am. 115 1424
[5]	Shawagfeh N T 2005 Appl. Math. Comput. 131 517
[6]	Duan J S, Rach R, Baleanu D and Wazwaz A M 2012 Commun. Frac. Calc. 2 73
[7]	Hristov J 2011 Eur. Phys. Spec. Top. 193 229
[8]	Hristov J 2010 Thermal Sci. 14 291
[9]	Wang Q 2008 Chaos, Solitons and Fractals 35 843
[10]	Kadem A and Baleanu D 2011 Rom. J. Phys. 56 332
[11]	Liu Q, Liu F, Turner I and Anh V 2007 J. Comput. Phys. 222 57
[12]	Zhuang P, Liu F, Anh V and Turner I 2009 SIAM. J. Num. Anal. 47 1760
[13]	Li C P, Zhao Z G and Chen Y Q 2011 Comput. Math. Appl. 62 855
[14]	He J H 1998 Comput. Method. Appl. M 167 57
[15]	He J H 1999 Int. J. Nonlinear Mech. 34 699
[16]	Podlubny I 1999 Fractional Differential Equations (New York: Academic press)
[17]	Kilbas A A, Srivastav H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (New York: Elsevier)
[18]	Debnath L and Dambaru B 2007 Integral Transforms and Their Applications (Boca Raton: Chapman & Hall/CRC Press)
[19]	Diethelm K 2010 The Analysis of Fractional Differential Equations (Berlin: Springer Verlag)
[20]	Metzler R and Klafter J 2000 Phys. Rep. 339 1
[21]	Lenzi E K, Malacarne L C, Mendes R S and Pedron I T 2003 Physica A 319245
[22]	Pedron I T, Mendes R S, Buratta T J, Malacarne L C and Lenzi, E K 2005 Phys. Rev. E 72 031106
[23]	Tadjerana C, Meerschaertb M M and Scheffler H P 2006 J. Comput. Phys. 213 205
[24]	Gorenfloa R, Mainardib F and Vivoli A 2007 Chaos, Solitons and Fractals 34 87
[25]	Carpinteri A and Sapora A 2010 Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik 90 203
[26]	Meilanov R, Shabanova M and Akhmedov E 2011 Int. Rev. Chem. Eng. 3 810
[27]	Sun H G, Chen W, Li C P and Chen Y Q 2012 Int. J. Bifur. Chaos 22 1250085
[28]	Wu G C 2011 Commun. Frac. Calc. 2 59
[29]	Wu G C and Wu K T 2012 Chin. Phys. Lett. 29 0605041
[30]	Das S 2009 Comput. Math. Appl. 57 483
[31]	Wu G C 2012 J. Appl. Math. 2012 ID 102850
[32]	Kong H 2012 Commun. Frac. Calc. 3 30
[33]	Allahviranloo T, Abbasbandy S and Rouhparvar H 2011 Appl. Soft. Comput. 11 2186
[34]	Jafari H and Baleanu D 2012 Cent. Eur. J Phys. 10 76
[35]	Jafari H and Khalique C M 2012 Commun. Frac. Calc. 3 38
[36]	Mo J Q, Lin W T and Wang H 2007 Chin. Phys. 16 951
[37]	Noor M A, Noor K I and Mohyud-Din S T 2009 Nonlinear Anal. Theor. Method Appl. 71 E630
[38]	Cao X Q, Song J Q, Zhang W M, Zhao J and Zhu X Q 2012 Acta Phys. Sin. 61 030203 (in Chinese)

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Variational iteration method for solving the time-fractional diffusion equations in porous medium

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