Damped oscillations in view of the fractional oscillator equation

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 18, 2002, Pages 1842011-1842018

  Ryabov, Ya E ^a,b   Puzenko, A ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b INSTITUTE OF MECHANICS AND ENGINEERING   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPLEX FORMATION; CRYSTALLIZATION; DERIVATIZATION; EVOLUTION; OSCILLATION; PHENOMENOLOGY; PHYSICAL PHENOMENA;

EID: 0036870768     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. A. Blumen, J. Klafter, and G. Zumofen, in Optical Spectroscopy of Glasses, edited by I. Zschokke (Reidel, Dordrecht, 1986).
2. M. Shlesinger, Annu. Rev. Phys. Chem. 39, 269 (1988).
3. M. Weissman, Rev. Mod. Phys. 60, 537 (1988).
4. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
5. H. Scher and E. Montroll, Phys. Rev. B 12, 2455 (1975).
6. U. Even, K. Rademann, J. Jortner, N. Manor, and R. Reisfeld, Phys. Rev. Lett. 52, 2164 (1984).
7. M. Cates, Phys. Rev. Lett. 53, 926 (1984).
8. H. Stanly, J. Stat. Phys. 36, 843 (1984).
9. H. Schiessel and A. Blumen, Fractals 3, 483 (1995).
10. G. Niklasson and C. Granqvist, Phys. Rev. Lett. 56, 256 (1986).
11. B. Berkowitz and H. Scher, Phys. Rev. Lett. 79, 4038 (1997).
12. A. Klemm, H. Müller, and R. Kimmih, Phys. Rev. E 55, 4413 (1997).
13. H. Berens and U. Westphal, Acta Sci. Math. (Szeged) 29, 93 (1968).
14. R. Nigmatullin, Phys. Status Solidi B 133,. 425 (1986).
15. W. Schneider and W. Wyss, J. Math. Phys. 30, 134 (1989).
16. T. Nonnenmacher, J. Phys. A 23, L697 (1990).
17. G. Jumarie, J. Math. Phys. 33, 3536 (1992).
18. Application of Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore, 2000).
19. R. Hilfer, J. Phys. Chem. B 104, 3914 (2000).
20. K.S. Cole and R.H. Cole, J. Phys. Chem. 9, 341 (1941).
21. R.R. Nigmatullin and Ya.E. Ryabov, Russ. Phys. J. 40, 314 (1997).
22. K. Weron and M. Kotulski, Physica A 232, 180 (1996).
23. K. Weron and A. Klauzer, Ferroelectrics 236, 59 (2000).
24. R. Hilfer, in Applications of Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore, 2000).
25. Ya.E. Ryabov, Yu. Feldman, N. Shinyashiki, and Sh. Yagihara, J. Phys. Chem. 116, 8610 (2002).
26. N. Shinyashiki, I. Arita, S. Yagihara, and S. Mashimo, J. Phys. Chem. B 102, 3249 (1998).
27. Ya. Ryabov, A. Gutina, V. Arkhipov, and Yu. Feldman, J. Phys. Chem. B 105, 1845 (2001).
28. Dielectric Spectroscopy of Polymeric Materials, edited by J. P. Runt and J. J. Fitzgerald (American Chemical Society, Washington, DC, 1997).
29. M. Antonietti, M. Neese, G. Blum, and F. Kremer, Langmuir 12, 4436 (1996).
30. J. Mijovic and J.W. Sy, Macromolecules 33, 9620 (2000).
31. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic Press, New York, 1974).
32. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications (Gordon and Breach, Amsterdam, 1993).
33. K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993).
34. P. L. Butzer and U. Westphal, in Applications of Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore, 2000).
35. R. Hilfer, Fractals 3, 549 (1995).
36. R. Hilfer, Physica A 221, 89 (1995).
37. B.N. Narahari Achar, J.W. Hanneken, T. Enck, and T. Clarke, Physica A 297, 361 (2001).
38. D. N. Zubarev, Nonequlibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974).
39. A. Prudnikov, Y. Brychkov, and O. Marichev, Integrals and Series (Gordon and Breach, New York, 1990).
40. R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962).