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[4] K. Falconer,
Fractal Geometry
, New York: John Wiley (1990).
[5] J. Feder,
Fractals
, New York: Plenum Press (1988).
[6] P. Grigolini, A. Rocco and B. J. West, “Fractional calculus as a macroscopic manifestation
of randomness,”
Phys. Rev. E
59
, 2603 (1999).
[7] L. Griffin, D. J. West and B. J. West, “Random stride intervals with memory,”
J. Biol. Phys
.
26
, 185-202 (2000).
[8] J. M. Hausdorff, C.-K. Peng, Z. Ladin
et al
. “Is walking a random walk? Evidence for long-
range correlations in stride interval of human gait,”
J. Appl. Physiol.
78
(1), 349-358 (1995).
[9] R.Hilfer,ed.,
Applications of Fractional Calculus in Physics
, Singapore: World Scientific
(2000).
[10] V. M. Kenkre, E. W. Montroll and M. F. Shlesinger, “Generalized master equations for
continuous-time random walks,”
J. Statist. Phys.
9
, 45 (1973).
[11] P. Lévy,
Théorie de l'addition des variables aléatoires
, Paris: Gauthier-Villars (1937)
[12] S. C. Lim and L. P. Teo, “Generalized Whittle-Matérn random field with application to
modeling,”
J. Phys.: Math. Theor
.
42
, 105202 (2009).
[13] E. Lutz, “Fractional Langevin equation,”
Phys. Rev. E
64
, 051106 (2001).
[14] R. L. Magin,
Fractional Calculus in Bioengineering
, Connecticut: Begell House (2006).
[15] F. Mainardi, R. Gorenflo and A. Vivoli, “Renewal processes of Mittag-Leffler and Wright
type,”
Fractional Calculus and Applied Analysis
8
, 7-38 (2005)
.
[16] B. B. Mandelbrot,
The Fractal Geometry of Nature
, San Francisco, CA: W. J. Freeman
(1983).
[17] P. Meakin,
Fractals, Scaling and Growth Far from Equilibrium
, Cambridge: Cambridge
University Press (1998).
[18] K. S. Miller and B. Ross,
An Introduction to the Fractional Calculus and Fractional
Differential Equations
, New York: John Wiley & Sons (1993).
[19] E. W. Montroll and G. H. Weiss, “Random walks on lattice. II,”
J. Math. Phys
.
6
, 167-181
(1965).
[20] C. K. Peng, J. Mietus, J. M. Hausdorff
et al
., “Long-range autocorrelations and non-
Gaussian behavior in the heartbeat,”
Phys. Rev. Lett.
70
, 1343 (1993).
[21] Yu. N. Rabotnov,
Elements of Hereditary Solid Mechanics
, Moscow: Mir (1980).
[22] A. Rocco and B. J. West, “Fractional calculus and the evolution of fractal phenomena,”
Physica A
265
, 535 (1999).
[23] D. Ruelle,
Chaotic Evolution and Strange Attractors
, Cambridge: Cambridge University
Press (1989).
[24] S. G. Samko, A. A. Kilbas and O. I. Marichev,
Fractional Integrals and Derivatives
,
Amsterdam: Gordon and Breach Science Publishers (1993).
[25] N. Scafetta, L. Griffin and B. J. West, “Hölder exponent spectra for human gait,”
Physica A
328
, 561-583 (2003).
[26] I. Sokolov, J. Klafter and A. Blumen, “Fractional kinetics,”
Physics Today
, Nov., 48-54
(2002).
[27] H. E. Stanley,
Introduction to Phase Transitions and Critical Phenomena
, Oxford: Oxford
University Press (1979).
[28] W. Weibull, “A statistical theory of strength of materials,”
Ing. Vetenskaps Akad. Handl. No.
151
(1939).
[29] G. Weiss,
Aspects and Applications of the Random Walk
, Amsterdam: North-Holland
(1994).
[30] B. J. West and T. Nonnenmacher, “An ant in a gurge,”
Phys. Lett. A
278
, 255-259 (2001).
