A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 375, Issue 42, 2011, Pages 3659-3663

  Wu, Guo Cheng ^a,b   Zhang, Sheng ^c  

^a Key Laboratory of Numerical Simulation of Sichuan Province   (China)

^b NEIJIANG NORMAL UNIVERSITY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Fractional differentiable functions; Fractional Hamiltonian system; Generalized Tu formula

Indexed keywords

CALCULATIONS;

AKNS HIERARCHY; DIFFERENTIABLE FUNCTIONS; GENERALIZED TU FORMULA; HAMILTONIAN HIERARCHIES; HAMILTONIAN STRUCTURES; HAMILTONIAN SYSTEMS; SOLITON EQUATION;

HAMILTONIANS;

EID: 80052965259     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2011.08.040     Document Type: Article

References (65)

1. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier Science B.V. Amsterdam
2. V. Kiryakova Generalized Fractional Calculus and Applications 1994 Longman Scientific & Technical Harlow copublished in the United States with John Wiley & Sons, Inc., New York
3. V. Lakshmikantham, and A.S. Vatsala Nonlinear Anal. 69 2008 2677
4. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley & Sons New York
5. I. Podlubny Fractional Differential Equation 1999 Academic Press San Diego
6. F. Riewe Phys. Rev. E 53 1996 1890
7. F. Riewe Phys. Rev. E 55 1997 3581
8. G.S.F. Frederico, and Delfim F.M. Torres Nonlinear Dyn. 53 2008 215
9. G.C. Wu Commun. Frac. Calc. 1 2010 27
10. D. Baleanu, and S.I. Muslih Phys. Scr. 72 2005 119
11. D. Baleanu, and O.P. Agrawal Czech J. Phys. 56 2006 1087
12. R.A. El-Nabulsi Fizika 14 2005 289
13. R.A. El-Nabulsi Int. J. Appl. Math. 17 2005 299
14. R.A. El-Nabulsi, and D.F.M. Torres J. Math. Phys. 49 2008 053521
15. O.P. Agrawal J. Phys. A: Math. Theor. 39 2006 10375
16. O.P. Agrawal J. Phys. A: Math. Theor. 40 2007 6287
17. V.E. Tarasov J. Phys. A: Math. Gen. 39 2006 8409
18. G. Jumarie Chaos Solitons Fract. 32 2007 969
19. R. Almeida, A.B. Malinowska, and D.F.M. Torres J. Math. Phys. 51 2010 033503
20. A.B. Malinowska, M.R.S. Ammi, and D.F.M. Torres Commun. Frac. Calc. 1 2010 32
21. J. Fujioka Phys. Lett. A 374 2010 1126
22. J. Fujioka Commun. Frac. Calc. 1 2010 1
23. G.Z. Tu J. Math. Phys. 30 1989 330
24. S. Purkait, and A.R. Chowdhury J. Phys. A: Math. Gen. 23 1990 L591
25. F.K. Guo, and Y.F. Zhang J. Phys. A: Math. Gen. 38 2005 8537
26. T.C. Xia, F.C. You, and D.Y. Chen Chaos Solitons Fract. 23 2005 1911
27. W.X. Ma, and B. Fuchssteiner Phys. Lett. A 213 1996 49
28. M.E. Nicholas, and T.L. Guadalupe Physica D 218 2006 105
29. W.X. Ma, X.X. Xu, and Y.F. Zhang J. Math. Phys. 47 2006 053501
30. W.X. Ma, and M. Chen J. Phys. A: Math. Gen. 39 2006 10787
31. K.M. Kolwankar, and A.D. Gangal Chaos 6 1996 505
32. K.M. Kolwankar, and A.D. Gangal Pramana J. Phys. 48 1997 49
33. K.M. Kolwankar, and A.D. Gangal Phys. Rev. Lett. 80 1998 214
34. W. Chen Chaos Solitons Fract. 28 2006 923
35. W. Chen, and H.G. Sun Mod. Phys. Lett. B 23 2009 449
36. J. Cresson J. Math. Phys. 44 2003 4907
37. J. Cresson J. Math. Anal. Appl. 307 2005 48
38. G. Jumarie Comput. Math. Appl. 51 2006 1367
39. A. Parvate, and A.D. Gangal Fractals 17 2009 53
40. G.C. Wu, and E.W.M. Lee Phys. Lett. A 374 2010 2506
41. G.C. Wu Comput. Math. Appl. 61 2011 2186
42. G.C. Wu Math. Comput. Model. 54 2011 2104
43. X.J. Yang, Research on fractal mathematics and some applications in mechanics, MS Thesis, China University of Mining and Technology, 2009 (in Chinese).
44. X. Li, M. Davison, C. Essex, On the concept of local fractional differentiation, preprint, http://www.apmaths.uwo.ca/mdavison/-library/ preprints/lfd2.pdf.
45. Y. Chen, Y. Yan, and K.W. Zhang J. Math. Anal. Appl. 362 2010 17
46. G. Jumarie Appl. Math. Lett. 22 2009 1659
47. A. Carpinteri, B. Chiaia, and P. Cornetti Z. Angew. Math. Mech. 84 2004 128
48. L. Nottale Fractal Space-Time and Microphysics 1993 World Scientific Singapore
49. L. Nottale Chaos Solitons Fract. 7 1996 877
50. G. Jumarie J. Appl. Math. Comput. 23 2007 215
51. F. Ben Adda C.R. Acad. Sci. Serié I. Math. 326 1998 931 (in French)
52. F. Ben Adda J. Fractional Calculus 11 1997 21
53. F. Ben Adda Nonlinear Anal. 47 2001 5423
54. K. Cottrill-Shepherd, and M. Naber J. Math. Phys. 42 2001 2203 math-ph/0301013
55. K. Cottrill-Shepherd, and M. Naber Fractional Differential Forms II preprint math-ph/0301016
56. Y. Chen, Z.Y. Yan, and H.Q. Zhang Appl. Math. Mech. 24 2003 256
57. K.K. Kazbekov Vladikavkaz Math. J. 7 2005 41 (in Russian)
58. V.E. Tarasov Ann. Phys. (N.Y.) 323 2008 2756
59. A. Carpinter, and A. Sapora ZAMM Z. Angew. Math. Mech. 90 2010 203
60. A. Carpinteri, and P. Cornetti Chaos Solitons Fract. 13 2002 85
61. A. Carpinteri, P. Cornetti, and K.M. Kolwankar Chaos Solitons Fract. 21 2004 623
62. M.S. El Naschie Chaos Solitons Fract. 25 2005 531
63. M.S. El Naschie Chaos Solitons Fract. 30 2006 579
64. Y.S. Liang, and W.Y. Su Chaos Solitons Fract. 34 2007 682
65. B.J. West, M. Bologna, and P. Grigolini Physics of Fractal Operators 2003 Springer-Verlag New York