Generalized Langevin equation with a three parameter Mittag-Leffler noise

Physica A: Statistical Mechanics and its Applications

Volumn 390, Issue 21-22, 2011, Pages 3627-3636

  Sandev, Trifce ^a   Tomovski, Živorad ^b   Dubbeldam, Johan L A ^c  

^a Radiation Safety Directorate   (Macedonia)

^b SS CYRIL AND METHODIUS UNIVERSITY   (Macedonia)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Anomalous diffusion; Displacement correlation function; Generalized Langevin equation; Three parameter Mittag Leffler noise; Time dependent diffusion coefficient; Velocity correlation function

Indexed keywords

DIFFUSION; LAPLACE TRANSFORMS;

ANOMALOUS DIFFUSION; CORRELATION FUNCTION; GENERALIZED LANGEVIN EQUATION; MITTAG-LEFFLER; TIME-DEPENDENT DIFFUSION COEFFICIENT; VELOCITY CORRELATION FUNCTIONS;

DIFFERENTIAL EQUATIONS;

EID: 80054890030     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2011.05.039     Document Type: Article

References (70)

1. R. Metzler, and J. Klafter Phys. Rep. 339 2000 1
2. R. Metzler, and J. Klafter J. Phys. A: Math. Gen. 37 2004 R161
3. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Publishing Company Singapore
4. R. Hilfer Physica A 329 2003 35
5. H. Yang, G. Luo, P. Karnchanaphanurach, T. Louie, I. Rech, S. Cova, L. Xun, and X.S. Xie Science 302 2003 262
6. S.C. Kou, and X.S. Xie Phys. Rev. Lett. 93 2004 180603
7. J. Tang, and R.A. Marcus Phys. Rev. Lett. 95 2005 107401
8. I. Golding, and E.C. Cox Phys. Rev. Lett. 96 2006 098102
9. S.C. Weber, A.J. Spakowitz, and J.A. Theriot Phys. Rev. Lett. 104 2010 238102
10. J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sørensen, L. Oddershede, and R. Metzler Phys. Rev. Lett. 106 2011 048103
11. N. Pottier, and A. Mauger Physica A 282 2000 77
12. E. Lutz Phys. Rev. E 64 2001 051106
13. N. Pottier Physica A 317 2003 371
14. P. Debnath, W. Min, X.S. Xie, and B.J. Cherayila J. Chem. Phys. 123 2005 204903
15. I. Goychuk, and P. Hnggi Phys. Rev. Lett. 99 2007 200601
16. I. Goychuk Phys. Rev. E 80 2009 046125
17. S. Burov, and E. Barkai Phys. Rev. E 78 2008 031112
18. R. Kubo Rep. Progr. Phys. 29 1966 255
19. R. Metzler, E. Barkai, and J. Klafter Phys. Rev. Lett. 82 1999 3563
20. T. Sandev, R. Metzler, and. Tomovski J. Phys. A: Math. Theor. 44 2011 255203
21. R. Metzler Phys. Rev. E 62 2000 6233
22. C.H. Eab, and S.C. Lim Physica A 389 2010 2510
23. S.C. Lim, and L.P. Teo J. Stat. Mech. 2009 P08015
24. F. Mainardi, and P. Pironi Extracta Math. 10 1996 140
25. G. Mittag-Leffler C. R. Acad. Sci., Paris 137 1903 554
26. A. Wiman Acta Math. 29 1905 191
27. R.P. Agarwal C. R. Acad. Sci., Paris 236 1953 2031
28. P. Humbert C. R. Acad. Sci., Paris 236 1953 1467
29. P. Humbert, and R.P. Agarwal Bull. Sci. Math. Ser. 2 1953 180
30. T.R. Prabhakar Yokohama Math. J. 19 1971 7
31. H.M. Srivastava, and. Tomovski Appl. Math. Comput. 211 2009 198
32. A.K. Shukla, and J.C. Prajapati J. Math. Anal. Appl. 336 2007 797
33. R.K. Saxena, A.M. Mathai, and H.J. Haubold Astrophys. Space Sci. 209 2004 299
34. R. Hilfer, and J. Seybold Integral Transforms Spec. Funct. 17 2006 637
35. I. Podlubny Fractional Differential Equations 1999 Acad. Press San Diego etc.
36. E. Capelas de Oliveira, F. Mainardi, and J. Vaz Jr. Eur. Phys. J. Spec. Top. 193 2011 161
37. F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanics A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer Verlag Wien and New York 291 348
38. F. Mainardi, F. Tampieri, Diffusion Regimes in Brownian Motion Induced by the Besset Hystory Force, Tech. Paper No. 8, FISBAT-TP-98/1, FISBAT-CNR, Bologna 22 June 1998, p. 20.
39. F. Mainardi, A. Mura, and F. Tampieri Mod. Probab. Stat. Phys. 9 2009 3
40. H. Scher, and E.W. Montroll Phys. Rev. B 12 1975 2455
41. Y. He, S. Burov, R. Metzler, and E. Barkai Phys. Rev. Lett. 101 2008 058101
42. S. Burov, J.-H. Jeon, R. Metzler, and E. Barkai Phys. Chem. Chem. Phys. 13 2011 1800
43. A.N. Kolmogorov Dokl. Acad. Sci. USSR 26 1940 115
44. J.L.A. Dubbeldam, A. Milchev, V.G. Rostiashvili, and T.A. Vilgis Europhys. Lett. 79 2007 18002
45. B.B. Mandelbrot, and J.W. Van Ness SIAM Rev. 10 1968 422
46. E.W. Montroll, and B.J. West E.W. Montroll, J.L. Lebowitz, Fluctuation Phenomena 2nd ed. 1987 Elsevier Publishing Comp., North Holland Personal Library
47. R. Mannella, P. Grigolini, and B.J. West Fractals 2 1994 81
48. J.L.A. Dubbeldam, V.G. Rostiashvili, A. Milchev, and T.A. Vilgis Phys. Rev. E 83 2011 011802
49. R. Metzler, and J. Klafter Biophys. J. 85 2003 2776
50. W. Deng, and E. Barkai Phys. Rev. E 79 2009 011112
51. R. Zwanzig Nonequilibrium Statistical Mechanics 2001 Oxford Univ. Press New York
52. W.T. Coffey, Yu.P. Kalmykov, and J.T. Waldron The Langevin Equation with Applications in Physics, Chemistry and Electrical Engineering 2nd ed. 2004 World Scientific Singapore p. 596 [1-edition 1996]
53. P. Langevin C. R. 146 1908 530
54. K.G. Wang Phys. Rev. A 45 1992 833
55. E. Lutz Europhys. Lett. 54 2001 293
56. A.D. Viales, and M.A. Despósito Phys. Rev. E 73 2006 016111
57. S. Burov, and E. Barkai Phys. Rev. Lett. 100 2008 070601
58. M.A. Despósito, and A.D. Viales Phys. Rev. E 77 2008 031123
59. M.A. Despósito, and A.D. Viales arXiv:0902.2786v1
60. A.D. Viales, and M.A. Despósito Phys. Rev. E 75 2007 042102
61. A.D. Viales, K.G. Wang, and M.A. Despósito Phys. Rev. E 80 2009 011101
62. R.F. Camargo, A.O. Chiacchio, R. Charnet, and E.C. de Oliveira J. Math. Phys. 50 2009 063507
63. R.F. Camargo, E.C. de Oliveira, and J. Vaz J. Math. Phys. 50 2009 123518
64. T. Sandev, and. Tomovski Phys. Scr. 82 2010 065001
65. R. Gorenflo, and F. Mainardi J. Phys.: Conf. Ser. 7 2005 1
66. W. Feller An Introduction to Probability Theory and Its Applications vol. II 1968 Wiley New York
67. A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi Higher Transcedential Functions vol. 3 1955 McGraw-Hill Book Company New York, Toronto and London
68. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematical Studies vol. 204 2006 Elsevier (North-Holland) Science Publishers Amsterdam
69. Tomovski, R. Hilfer, and H.M. Srivastava Integral Transforms Spec. Funct. 21 2010 797
70. T.J. Bromwich An Introduction to the Theory of Infinite Series 1949 MacMillan and Co.