Fractional calculus and the evolution of fractal phenomena

Physica A: Statistical Mechanics and its Applications

Volumn 265, Issue 3, 1999, Pages 535-546

  Rocco, Andrea ^a   West, Bruce J ^a  

^a UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); EQUATIONS OF MOTION; FUNCTIONS; RANDOM PROCESSES;

FRACTIONAL CALCULUS; GENERALIZED WEIERSTRASS FUNCTION (GWF);

FRACTALS;

EID: 0032665134     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00550-0     Document Type: Article

References (33)

1. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1977.
2. B.J. West, Physiology, Promiscuity and Prophecy at the Millennium: A Tale of Tails, Studies of Nonlinear Phenomena in the Life Sciences, vol. 9, World Scientific, Singapore, 1998.
3. P. Meakin, Fractals, Scaling and Growth Far from Equilibrium, Cambridge Nonlinear Science Series 5, Cambridge University Press, Cambridge, 1998.
4. M. Schroeder, Fractals, Chaos, Power Laws, Freeman, New York, 1991.
5. L.F. Richardson, Proc. Roy. Soc. London A 110 (1926) 709.
6. Shlesinger M.F., West B.J., Klafter J. Phys. Rev. Lett. 58:1987;1100.
7. P. Lévy, Calcul des Probabilities, Guthier-Villars, Paris, 1925; Théorie de l'Addition des Variables Aléatoires, Guthier, Paris, 1937.
8. P. Lévy, Calcul des Probabilities, Guthier-Villars, Paris, 1925; Théorie de l'Addition des Variables Aléatoires, Guthier, Paris, 1937.
9. B.D. Hughes, Random Walks and Random Environments, vol. 1: Random Walks, Oxford Science Publications, Clarendon Press, Oxford, 1995.
10. E.W. Montroll, B.J. West, in: E.W. Montroll, J.L. Lebowitz (Eds.), Fluctuation Phenomena, 2nd ed., North-Holland Personal Library, North-Holland, Amsterdam, 1987, pp. 61-206.
11. E.W. Montroll, M.F. Shlesinger, in: E.W. Montroll, J.L. Lebowitz (Eds.), Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, North-Holland, Amsterdam, 1983, pp. 1-121.
12. P. Langevin, C.R. Acad. Sci. Paris 530 (1908).
13. J. Perrin, Mouvement brownien et réalité molé culaire, Annales de Chimie et de Physique VIII 18 (1909) 5-114. Translated by F. Soddy as Brownian Movement and Molecular Reality, Taylor and Francis, London, 1912.
14. J. Perrin, Mouvement brownien et réalité molé culaire, Annales de Chimie et de Physique VIII 18 (1909) 5-114. Translated by F. Soddy as Brownian Movement and Molecular Reality, Taylor and Francis, London, 1912.
15. Doob J.L. Ann. Math. 43:1942;351.
16. Uhlenbeck G.E., Ornstein L.S. Phys. Rev. 36:1930;823.
17. P. Grigolini, A. Rocco, B.J. West, Phys. Rev. E, to appear.
18. Allegrini P., Grigolini P., West B.J. Phys. Rev. E 54. 1996:4760.
19. Compte A. Phys. Rev. E. 53:1996;4191.
20. Chaves A.S. Phys. Lett. A. 239:1998;13.
21. Hosking J.T.M. Biometrika. 68:1981;165.
22. J. Bernan, Statistics of Long-Memory Processes, Monograph on Statistics and Applied Probability, vol. 61, Chapman and Hall, New York, 1994.
23. B.J. West, P. Grigolini, in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 1998.
24. Glöckle W.G., Nonnenmacher T.F. Rheol. Acta. 33:1994;337.
25. Berry M. J. Phys. A. 12:1979;781.
26. Schneider W.R., Wyss W. J. Math. Phys. 30:1989;134.
27. Glöckle W.G., Nonnenmacher T.F. J. Stat. Phys. 71:1993;741.
28. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, vols. 1 and 2, MIT Press, Cambridge, MA, 1971.
29. K. Falconer, Fractal Geometry, Wiley, New York, 1990.
30. Berry M.V., Lewis Z.V. Proc. Roy. Soc. Lond. A. 370:1980;459.
31. Mauldin R.D., Williams S.C. Trans. Am. Math. Soc. 298:1986;793.
32. Kolwankar K.M., Gangal A.D. Chaos. 6:1996;505.
33. Kolwankar K.M., Gangal A.D. Pramana J. Phys. 48:1997;49.