Solving the fractional BBM-Burgers equation using the homotopy analysis method

Chaos, Solitons and Fractals

Volumn 40, Issue 4, 2009, Pages 1616-1622

  Song, Lina ^a   Zhang, Hongqing ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS;

APPROXIMATION SOLUTION; COMPUTABLE COMPONENTS; CONVERGENT SERIES; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; HOMOTOPY ANALYSIS METHODS; INITIAL CONDITIONS; NUMERICAL SOLUTION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 65449123574     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.09.042     Document Type: Article

References (39)

1. Ablowitz M.J., and Clarkson P.A. Solitons, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press, New York
2. Wadat M. J Phys Soc Jpn 32 (1972) 1681
3. Wadat M. J Phys Soc Jpn 34 (1972) 1280
4. Wadat M., Sanuki H., and Konno K. Prog Theor Phys 53 (1975) 419
5. Wadati M. J Phys Soc Jpn 38 (1975) 673
6. Wadati M. J Phys Soc Jpn 38 (1975) 681
7. Matveev V.B., and Salle M.A. Darbooux transformation and soliton (1991), Springer, Berlin
8. Hirota R. The direct method in soliton theory (2004), Cambridge University Press, New York
9. Conte R., and Musette M. J Phys A: Math Gen 22 (1989) 169
10. Clarkson P.A., and Kruskal M.D. J Math Phys 30 (1989) 2201
11. Lou S.Y., Chen C.L., and Tang X.Y. J Math Phys 43 (2002) 4078
12. Liu S.K., Fu Z.T., Liu S.D., and Zhao Q. Phys Lett A 289 (2001) 69
13. He J.H., and Wu X.H. Chaos Solitons & Fractals 30 (2006) 700
14. Fan E.G., and Chao L. Phys Lett A 285 (2001) 373
15. Yan Z.Y. Phys Lett A 285 (2001) 355
16. Lü Z.S. Chaos Solitons & Fractals 17 (2003) 669
17. Li B., Chen Y., and Zhang H.Q. Chaos Solitons & Fractals 15 (2003) 647
18. Chen Y., Zheng X.D., Li B., and Zhang H.Q. Appl Math Comput 149 (2004) 277
19. Xie F.D., Zhang Y., and Lü Z.S. Chaos Solitons & Fractals 24 (2005) 257
20. Wang Q., and Chen Y. Chaos Solitons & Fractals 30 (2006) 197
21. Song L.N., and Zhang H.Q. Appl Math Comput 180 (2006) 664
22. Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis. Shanghai Jiao Tong University; 1992.
23. Liao S.J. Int J Non-linear Mech 34 (1999) 759
24. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method (2003), Chapman & Hall/CRC Press, Boca Raton
25. Liao S.J. J Fluid Mech 488 (2003) 189
26. Liao S.J. Appl Math Comput 147 (2004) 499
27. Liao S.J. Int J Heat Mass Transfer 48 (2005) 2529
28. Liao S.J. Appl Math Comput 169 (2005) 1186
29. Liao S.J., Su J., and Chwang A.T. Int J Heat Mass Transfer 49 (2006) 2437
30. Liao S.J., and Magyari E. Z Angew Math Phys 57 (2006) 777
31. Liao S.J. Stud Appl Math 117 (2006) 239
32. Abbasbandy S. Phys Lett A 360 (2006) 109
33. Zhu S.P. ANZIAM J 47 (2006) 477
34. Abbasbandy S. Phys Lett A 361 (2007) 478
35. West B.J., Bolognab M., and Grigolini P. Physics of fractal operators (2003), Springer, New York
36. Miller K.S., and Ross B. An introduction to the fractional calculus and fractional differential equations (1993), Wiley, New York
37. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional integrals and derivatives: theory and applications (1993), Gordon and Breach, Yverdon
38. Podlubny I. Fractional differential equations (1999), Academic Press, San Diego
39. Caputo M. J Roy Astr Soc 13 (1967) 529