Accelerating and retarding anomalous diffusion

Journal of Physics A: Mathematical and Theoretical

Volumn 45, Issue 14, 2012, Pages

  Eab, Chai Hok ^a   Lim, S C ^b  

^a CHULALONGKORN UNIVERSITY   (Thailand)

^b MULTIMEDIA UNIVERSITY   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858979441     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/14/145001     Document Type: Article

References (74)

1. Metzler R and Klafter J 2000 Phys. Rep. 339 177
2. Klages R, Radons G and Sokolov I M (ed) 2008 Anomalous Transport: Foundations and Applications (New York: Wiley)
3. Klafter J, Lim S C and Metzler R (ed) 2011 Fractional Dynamics: Recent Advances (Singapore: World Scientific)
4. Seshadri V and West B J 1982 Proc. Natl Acad. Sci. USA 79 45015
5. Krger J and Ruthven D M 1992 Diffusion in Zeolites and other Microporous Solids (New York: Wiley)
6. Saxton M J 1996 Biophys. J. 70 1250
7. Weiss M, Elsner M, Kartberg F and Nilsson T 2004 Biophys. J. 87 3518
8. Khan S, Reynolds A M, Morrison I E G and Cherry R J 2005 Phys. Rev. E 71 041915
9. Bronstein I et al 2009 Phys. Rev. Lett. 103 018102
10. Bergholz W, Hutchison J L and Pirouz P 1985 J. Appl. Phys. 58 341924
11. Agarwal A, Gossmann H J, Eaglesham D J, Herner S B and Fiory A T 1999 Appl. Phys. Lett. 74 2435
12. Tan T Y and Gsele U 2005 Diffusion in Condensed Matter: Methods, Materials, Models 2nd edn ed P Heitjans and J Krger (New York: Springer) pp 165208
13. Kirk J G, Duffy P and Gallant Y A 1996 Astron. Astrophys. 314 1010
14. Perri S and Zimbardo G 2007 Astrophys. J. Lett. 671 L177
15. Geisel T, Nierwetberg J and Zacheri A 1985 Phys. Rev. Lett. 54 616
16. Furtado F, Glimm J, Lindquist B, Pereira F and Zhang Q 1992 Time Dependent Anomalous Diffusion for Flow in Multi-Fractal Porous Media vol 398 (New York: Springer) p 79
17. Glimm J, Lindquist W B B, Pereira F and Zhang Q 1993 Transp. Porous Media 13 97122
18. Peiltier R and Ĺvy V́hel J 1995 Rapport Technique Inria 2645
19. Benassi A, Jaffard S and Roux D 1997 Rev. Mat. Iberoamericana 13 19
20. Lim S C 2001 J. Phys. A: Math. Gen. 34 130110
21. Ross B and Samko S 1993 Integral Trans. Spec. Funct. 1 277300
22. Samko S 1995 Anal. Math. 21 21336
23. Lorenzo C F and Hartley T T 2002 Nonlinear Dyn. 29 5798
24. Kobelev Ya L, Kobelev L Ya and Klimontovich Yu L 2003 Dokl. Phys. 48 2648
25. Chechkin A V, Gorenflo R and Sokolov I M 2005 J. Phys. A.: Math Gen. 38 L67984
26. Sun H, Chen W and Chen Y Q 2009 Physica A 297 458692
27. Caputo M 1967 J. R. Astron. Soc. 13 52939
28. Caputo M 2001 Fract. Calc. Appl. Anal. 4 42142
29. Chechkin A, Gorenflo R and Sokolov I 2002 Phys. Rev. E 66 046129
30. Chechkin A V, Gorenflo R, Sokolov I M and Gonchar V Y 2002 Fract. Calc. Appl. Anal. 6 25979
31. Meerschaert M M and Scheffler H P 2006 Stoch. Process. Appl. 116 121535
32. Mainardi F, Mura A, Pagnini G and Gorenflo R 2008 J. Vib. Control 14 126790
33. Eab C H and Lim S C 2011 Phys. Rev. E 83 031136
34. Samko S, Kilbas A A and Maritchev D I 1993 Integrals and Derivatives of the Fractional Order and Some of Their Applications (Armsterdam: Gordon and Breach)
35. Podlubny I 1999 Fractional Differential Equations (San Diego: Academic)
36. West B, Bologna M and Grigolini P 2003 Physics of Fractal Operators (New York: Springer)
37. Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
38. Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity (London: Imperial College Press)
39. Gelfand I M and Shilov G E 1964 Generalized Functions: Properties and Operations vol 1 (New York: Academic)
40. Gelfand I M and Vilenkin N Ya 1964 Generalized Functions: Applications of Harmonic Analysis vol 4 (New York: Academic)
41. Qian H 2003 Processes with Long Range Correlations (Lecture Notes in Physics vol 621) ed G Rangarajan and M Ding (New York: Springer) p 22
42. Barton R J and Poor H V 1988 IEEE Trans. Inform. Theory 34 94359
43. Zinde-Walsh V and Phillips P C B 2003 Probability, Statistics and Their Applications: Papers in Honor of Rabi Bhattacharya ed K Athreya (Beachwood, OH: Institute of Mathematical Statistics) pp 28592
44. Mushura Y 2008 Stochastic Calculus for Fractional Brownian Motion and Related Processes (Lecture Notes in Mathematics vol 1929) (New York: Springer)
45. F Biagini Y H and ksendal B 2008 Stochastic Calculus for Fractional Brownian Motion and Applications (New York: Springer)
46. Azmoodeh E, Tikanmki H and Valkeila E 2010 Stat. Probab. Lett. 80 154350
47. Gradshteyn I S and Ryzhik I M 1994 Table of Integrals, Series, and Products 5th edn (New York: Academic)
48. Cheridito P 2001 Bernoulli 7 91334
49. El-Nouty C 2003 Stat. Probab. Lett. 65 11120
50. Thale C 2009 Appl. Math. Sci. 3 1885901
51. Doukhan P, Oppenheim G and Taqqu M S (ed) 2003 Theory and Applications of Long-Range Dependence (New York: Birkhuser)
52. Lim S C and Muniandy S V 2003 J. Phys. A: Math. Gen. 36 3961
53. Benassi A, Bertrand P, Cohen S and Istas J 2000 Stat. Inference Stoch. Process. 3 101
54. Ayache A, Bertrand P and Ĺvy V́hel J 2007 Stat. Inference Stoch. Process. 10 1
55. Lim S C and Teo L P 2009 J. Stat. Mech. 2009 P08015
56. Vestergaard-Bogind B, Stampe P and Christophersen P 1985 J. Membr. Bio. 88 6775
57. Wei Q H, Bechinger C and Leiderer P 2000 Science 287 6257
58. Servidori M et al 1987 J. Appl. Phys. 61 183440
59. Erd́lyi A, Magnus W, Oberhettinger F and Tricomi F G (ed) 1955 Higher Transcendental Functions vol 3 (New York: McGraw-Hill)
60. Eab C H and Lim S C 2010 Physica A 389 251021
61. Eab C H and Lim S C in preparation
62. Bel G and Barkai E 2005 Phys. Rev. Lett. 94 240602
63. Deng W and Barkai E 2009 Phys. Rev. E 79 011112
64. Fulinski A 2011 Phys. Rev. E 83 061140
65. Burov S, Jeon J-H, Metzler R and Barkai E 2011 Phys. Chem. Chem. Phys. 13 1800
66. Wong I Y et al 2004 Phys. Rev. Lett. 92 178101
67. Szymanski J and Weiss M 2009 Phys. Rev. Lett. 103 038102
68. Tejedor V et al 2010 Biophys. J. 98 1364
69. Jeon J-H, Tejedor V, Burov S, Barkai E, Selhuber-Unkel C, Berg-Srensen K, Oddershede L and Metzler R 2011 Phys. Rev. Lett. 106 048103
70. Golding I and Cox E C 2006 Phys. Rev. Lett. 96 098102
71. Magdziarz M, Weron A, Burnecki K and Klafter J 2009 Phys. Rev. Lett. 103 180602
72. Burnecki K and Weron A 2010 Phys. Rev. E 82 021130
73. Kepten E, Bronshtein I and Garini Y 2011 Phys. Rev. E 83 041919
74. Weigel A V et al 2011 Proc. Natl Acad. Sci. 108 6438