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

Chinese Physics B

Volumn 21, Issue 12, 2012, Pages

  Wu, Guo Cheng ^a,b  

^a NEIJIANG NORMAL UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Captuo derivative; Laplace transform; Riemann Liouville derivative; time fractional diffusion equation; variational iteration method

Indexed keywords

ARBITRARY ORDER; DIFFUSION MODEL; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; POROUS MEDIUM; TIME-FRACTIONAL DIFFUSION; VARIATIONAL ITERATION METHOD;

LAGRANGE MULTIPLIERS; LAPLACE TRANSFORMS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS;

ITERATIVE METHODS;

EID: 84870873877     PISSN: 16741056     EISSN: None     Source Type: Journal    
DOI: 10.1088/1674-1056/21/12/120504     Document Type: Article

References (38)

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. 3 802
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 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 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)