Fractional kinetic equations: Solutions and applications

Chaos

Volumn 7, Issue 4, 1997, Pages 753-764

  Saichev, Alexander I ^a   Zaslavsky, George M ^b,c  

^a LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

^b NEW YORK UNIVERSITY   (United States)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000599032     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166272     Document Type: Article

References (35)

1. G. M. Zaslavsky, in Topological Aspects of The Dynamics of Fluids and Plasmas, edited by H. K. Moffatt, G. M. Zaslavsky, P. Compte, and M. Tabor (Kluwer, Boston, 1992), p. 481; Chaos 4, 25 (1994); Physica D 76, 110 (1994).
2. G. M. Zaslavsky, in Topological Aspects of The Dynamics of Fluids and Plasmas, edited by H. K. Moffatt, G. M. Zaslavsky, P. Compte, and M. Tabor (Kluwer, Boston, 1992), p. 481; Chaos 4, 25 (1994); Physica D 76, 110 (1994).
3. G. M. Zaslavsky, in Topological Aspects of The Dynamics of Fluids and Plasmas, edited by H. K. Moffatt, G. M. Zaslavsky, P. Compte, and M. Tabor (Kluwer, Boston, 1992), p. 481; Chaos 4, 25 (1994); Physica D 76, 110 (1994).
4. G. M. Zaslavsky, M. Edelman, and B. Nyazov, Chaos 7, 159 (1997).
5. G. M. Zaslavsky, D. Stevens, and H. Weitzner, Phys. Rev. E 48, 1683 (1993); S. Benkadda, S. Kassibrakis, R. White, and G. M. Zaslavsky, Phys. Rev. E 55, 4909 (1997).
6. G. M. Zaslavsky, D. Stevens, and H. Weitzner, Phys. Rev. E 48, 1683 (1993); S. Benkadda, S. Kassibrakis, R. White, and G. M. Zaslavsky, Phys. Rev. E 55, 4909 (1997).
7. P. Lévy, Theorie de l'Addition des Variables Aletoires (Gauthier-Villiers, Paris, 1937).
8. J.-P. Kahane, in Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch (Springer, New York, 1995), p. 99.
9. E. W. Montroll and M. F. Shlesinger, in Studies in Statistical Mechanics, edited by J. Lebowitz and E. W. Montroll (North-Holland, Amsterdam, 1984), Vol. 11, p. 1.
10. M. F. Shlesinger, Annu. Rev. Phys. Chem. 39, 269 (1988); Physica D 38, 304 (1989).
11. M. F. Shlesinger, Annu. Rev. Phys. Chem. 39, 269 (1988); Physica D 38, 304 (1989).
12. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).
13. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
14. M. F. Shlesinger, J. Klafter, and Y. M. Wong, J. Stat. Phys. 27, 499 (1982); M. F. Shlesinger and J. Klafter, Phys. Rev. E 54, 2551 (1985).
15. M. F. Shlesinger, J. Klafter, and Y. M. Wong, J. Stat. Phys. 27, 499 (1982); M. F. Shlesinger and J. Klafter, Phys. Rev. E 54, 2551 (1985).
16. V. V. Afanas'ev, R. Z. Sagdeev, and G. M. Zaslavsky, Chaos 1, 143 (1991).
17. R. Balescu. Phys. Rev. E 55, 2465 (1997).
18. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 935 (1977).
19. E. A. Novikov, in Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch (Springer, New York, 1995), p. 35.
20. R. R. Nigmatullin, Phys. Status Solidi B 124, 389 (1984).
21. F. Mainardi, J. Alloys Compd. 211/212, 534 (1994); Chaos Solitons Fractals 7, 17 (1996).
22. F. Mainardi, J. Alloys Compd. 211/212, 534 (1994); Chaos Solitons Fractals 7, 17 (1996).
23. I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1.
24. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Their Applications (Nauka i Tekhnika, Minsk, 1987). (Translation by Harwood Academic).
25. K. S. Miller and B. Ross, An Introduction to the Fractional Differential Equations (Wiley, New York, 1993).
26. A. I. Saichev and W. A. Woyczyński, Distributions in the Physical and Engineering Sciences, (Birkhäuser, Boston, 1997), Vol. 1.
27. V. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1971), Vol. 2.
28. A. Erdelyi, Ed., Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 2; Higher Transcendental Functions (McGraw-Hill, New York, 1955), Vol. 3.
29. A. Erdelyi, Ed., Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 2; Higher Transcendental Functions (McGraw-Hill, New York, 1955), Vol. 3.
30. B. V. Gnedenko, The Theory of Probability (Chelsea, New York, 1963).
31. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett. 58, 1100 (1987); J. Klafter, A. Bluman, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987).
32. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett. 58, 1100 (1987); J. Klafter, A. Bluman, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987).
33. V. M. Zolotarev, One-dimensional Stable Distributions (American Mathematical Society, Providence, 1986).
34. R. Hilfer and L. Anton, Phys. Rev. E 51, R848 (1995).
35. R. Balescu, Statistical Dynamics; Matter Out of Equilibrium (Imperial College Press, World Scientific, Singapore, 1997).