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1 R. Hilfer, Fractional dynamics, irreversibility and ergodicity breaking, Chaos, Solitons & Fractals. 5, 1475, (1995).
2 K. Oldham and J. Spanier, The Fractional Calculus. (Academic Press, New York, 1974).
3 B. Ross, The development of fractional calculus 1695-1900, Historia Mathematica. 4, 75, (1977).
4 S. Samko, A. Kilbas, and O. Marichev, Fractional Integrals and Derivatives. (Gordon and Breach, Berlin, 1993).
5P. Butzer and U. Westphal. Introduction to fractional calculus. In ed. R. Hilfer, Applications of Fractional Calculus in Physics, p. 1, Singapore, (2000). World Scientific.
6 R. Hilfer. Threefold introduction to fractional derivatives. In eds. R. Klages, G. Radons, and I. Sokolov, Anomalous Transport: Foundations and Applications, pp. 17–74, Weinheim, (2008). Wiley-VCH.
7 S. Bochner, Harmonic Analysis and the Theory of Probability. (University of California Press, Berkeley, 1955).
8 A. Balakrishnan, Fractional powers of closed operators and the semigroups generated by them, Pacific J. Math. 10, 419, (1960).
9 K. Yosida, Fractional powers of infinitesimal generators and the analyticity of the semi-groups generated by them, Proc.Japan Acad. 36, 86, (1960).
10 T. Kato, Note on fractional powers of linear operators, Proc.Japan Acad. 36, 94, (1960).
11 H. Komatsu, Fractional powers of operators, Pacific Journal of Mathematics. 19, 285, (1966).
12 H. Komatsu, Fractional powers of operators II: Interpolation spaces, Pacific Journal of Mathematics. 21, 89, (1967).
13 U. Westphal, Ein Kalkül für gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren. Teil I: Halbgruppenerzeuger, Compositio Math. 22, 67, (1970).
14 U. Westphal, An approach to fractional powers of operators via fractional differences, Proc. London Math. Soc. 29, 557, (1974).
15 O. Lanford and D. Robinson, Fractional powers of generators of equicontinuous semigroups and fractional derivatives, J. Austral. Math. Soc.(A). 46, 473–504, (1989).
16 U. Westphal. Fractional powers of infinitesimal generators of semigroups. In ed. R. Hilfer, Applications of Fractional Calculus in Physics, p. 131, Singapore, (2000). World Scientific.
17 R. Hilfer, Applications of Fractional Calculus in Physics. (World Scientific Publ. Co., Singapore, 2000).
18 R. Hilfer, R. Metzler, A. Blumen, and J. Klafter(eds), Strange Kinetics, Chemical Physics. 284, (2002).
19 R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys.Rep. 339, 1, (2000).
20 R. Klages et al., Anomalous Transport. (Wiley-VCH, Weinheim, 2008).
21R. Hilfer, Foundations of fractional dynamics, Fractals. 3, 549, (1995).
22 W. Ross, Aristotelis Physica. Recognovit brevique adnotatione critica instruxit W.D. Ross. (Oxford University Press, Oxford, 1950).
23 P. Mohr, B. Taylor, and D. Newell, CODATA recommended values of the fundamental physical constants: 1998, J. Phys. Chem. Ref. Data. 37, 1187, (2008).
24 I. Newton, Philosophiae Naturalis Principia Mathematica. (Societas Regia ac Joseph Streater, London, 1687).
25 N. Bhatia and G. Szegö, Stability Theory of Dynamical Systems. (Springer, Berlin, 1970).
26 I. Cornfeld, S. Fomin, and Y. Sinai, Ergodic Theory. (Springer, Berlin, 1982).
27B. Mandelbrot, The Fractal Geometry of Nature. (Freeman, San Francisco, 1982).
28 A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. (Springer, Berlin, 1983).
29 E. Hille and R. Phillips, Functional Analysis and Semi-Groups. (American Mathematical Society, Providence, 1957).
30 O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I. (Springer, Berlin, 1979).
31 W. Thirring, Lehrbuch der Mathematischen Physik 3: Quantenmechanik von Atomen und Molekülen. (Springer, Wien, 1979).
32 J. Neerven, The Adjoint of a Semigroup of Linear Operators. (Springer, Berlin, 1992).
33 R. Phillips, On the generation of semigroups of linear operators, Pacific J. Math. 2, 343, (1952).
34 J. Lebowitz, Statistical mechanics: A selective review of two central issues, Rev.Mod.Phys. 71, S346, (1999).
35 R. Hilfer, Thermodynamic scaling derived via analytic continuation from the classification of Ehrenfest, Physica Scripta. 44, 321, (1991).
36 R. Hilfer, Multiscaling and the classification of continuous phase transitions, Phys. Rev. Lett. 68, 190, (1992).
37 R. Hilfer, Scaling theory and the classification of phase transitions, Mod. Phys. Lett. B. 6, 773, (1992).
38 R. Hilfer, Classification theory for anequilibrium phase transitions, Phys. Rev. E. 48, 2466, (1993).
39 R. Hilfer. On a new class of phase transitions. In eds. W. Beyermann, N. Huang-Liu, and D. MacLaughlin, Random Magnetism and High-Temperature Superconductivity, p. 85, Singapore,, (1994). World Scientific Publ. Co.
40 S. Kakutani, Induced measure preserving transformations, Proceedings of the Japan Academy, Series A. 19, 635, (1943).
41 H. Bauer, Maß- und Integrationstheorie. (Walter de Gruyter, Berlin, 1992).
42 B. Gnedenko and A. Kolmogorov, Limit Distributions for Sums of Independent Random Variables. (Addison-Wesley, Cambridge, 1954).
43 H. Bergström, Limit Theorems for Convolutions. (Wiley, New York, 1963).
44 W. Feller, An Introduction to Probability Theory and Its Applications. vol. II, (Wiley, New York, 1971).
45 I. Ibragimov and Y. Linnik, Independent and Stationary Sequences of Random Variables. (Wolters-Nordhoff Publishing, Groningen, 1971).
46 E. Seneta, Regularly Varying Functions. (Springer Verlag, Berlin, 1976).
47 S. Bochner, Diffusion equation and stochastic processes, Proc. Natl. Acad. Sci. USA. 35, 368, (1949).
48 E. Nelson, A functional calculus using singular Laplace integrals, Trans. Amer. Math. Soc. 88, 400, (1958).
49 R. Hilfer. Remarks on fractional time. In eds. L. Castell and O. Ischebeck, Time, Quantum and Information, p. 235, Berlin, (2003). Springer.
50 R. Hilfer. Fractional time evolution. In ed. R. Hilfer, Applications of Fractional Calculus in Physics, p. 87, Singapore, (2000). World Scientific.
51 A. Marchaud, Sur les derivees et sur les differences des fonctions de variables reelles, Journal de Mathematiques Pures et Appliquees. 6, 337, (1927).
52 J. Stafney, Integral representations of fractional powers of infinitesimal generators, Illinois Journal of Mathematics. 20, 124, (1976).
53 R. Hilfer, Fitting the excess wing in the dielectric \alpha-relaxation of propylene carbonate, J.Phys.: Condens. Matter. 14, 2297, (2002).
54 R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials, Chem.Phys. 284, 399, (2002).
55 P. Lunkenheimer, U. Schneider, R. Brand, and A. Loidl, Glassy dynamics, Contemporary Physics. 41, 15, (2000).
56 U. Schneider, P. Lunkenheimer, R. Brand, and A. Loidl, Broadband dielectric spectoscopy on glass-forming propylene carbonate, Phys.Rev. E. 59, 6924, (1999).
57 D. Davidson and R. Cole, Dielectric relaxation in glycerol, propylene glycol and n-propanol, J.Chem.Phys. 19, 1484, (1951).
58 R. Hilfer, Analytical representations for relaxation functions of glasses, J. Noncryst. Solids. 305, 122, (2002).
59 S. Havriliak and S. Negami, A complex plane analysis of \alpha-dispersions in some polymer systems, Journal of Polymer Sciene: Part C. 14, 99–117, (1966).
60 R. Hilfer, H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems, Phys.Rev.E. 65, 061510, (2002).
61 R. Hilfer, Y. Luchko, and Z. Tomovski, Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives, Fractional Calculus and Applied Analysis. 12, 299, (2009).
62 F. Kremer and A. Schönhals(eds.), Broad Band Dielectric Spectroscopy. (Springer Verlag, Berlin, 2003).
63 G. Zaslavsky. Fractional kinetics of hamiltonian chaotic systems. In ed. R. Hilfer, Applications of Fractional Calculus in Physics, p. 202, Singapore, (2000). World Scientific.
64 P. Inizan. Dynamique Fractionnaire Pour Le Chaos Hamiltonien. PhD thesis, L’Observatoire de Paris, (2011).
65 M. Riesz, L’integrale de Riemann-Liouville et le probleme de Cauchy, Acta mathematica. 81, 1, (1949).
66 E. Montroll and G. Weiss, Random walks on lattices. II, J. Math. Phys. 6, 167, (1965).
67 M. Barber and B. Ninham, Random and Restricted Walks. (Gordon and Breach Science Publ., New York, 1970).
68 E. Montroll and H. Scher, Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries, J. Stat. Phys. 9, 101, (1973).
69 R. Hilfer and R. Orbach, Continuous time random walk approach to dynamic percolation, Chem.Phys. 128, 275, (1988).
70 B. Hughes, Random Walks and Random Environments. vol. 1, (Clarendon Press, Oxford, 1995).
71 R. Hilfer and L. Anton, Fractional master equations and fractal time random walks, Phys.Rev.E, Rapid Commun. 51, R848, (1995).
72 R. Hilfer, Exact solutions for a class of fractal time random walks, Fractals. 3(1), 211, (1995).
73 I. Sokolov, J. Klafter, and A. Blumen, Fractional kinetics, Physics Today. Nov.2002, 48, (2002).
74 A. V. Balakrishnan, Anomalous diffusion in one dimension, Physica. 132A, 569–580, (1985).
75 M. Shlesinger, Asymptotic solutions of continuous time random walks, J. Stat. Phys. 10, 421, (1974).
76 R. Hilfer. On fractional diffusion and its relation with continuous time random walks. In eds. A. P. R. Kutner and K. Sznajd-Weron, Anomalous Diffusion: From Basis to Applications, p. 77, Berlin, (1999). Springer.
77 R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives, J.Phys.Chem.B. 104, 3914, (2000).
78 R. Hilfer, On fractional diffusion and continuous time random walks, Physica A. 329, 35, (2003).
79 A. Compte, Stochastic foundations of fractional dynamics, Phys.Rev. E. 55, 4191, (1996).
80 R. Metzler, J. Klafter, and I. Sokolov, Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended, Phys.Rev.E. 58, 1621, (1998).
81 R. Metzler, E. Barkai, and J. Klafter, Anomalous diffusion and relaxation close to equilibrium: A fractional Fokker-Planck equation approach, Phys.Rev.Lett. 82, 3563, (1999).
82 I. Sokolov, Thermodynamics and fractional fokker-planck equations, Phys.Rev.E. 63, 056111, (2001).
83 M. Meerschaert, D. Benson, H. Scheffler, and P. Becker-Kern, Governing equations and solutions of anomalous random walk limits, Phys.Rev.E. 66, 060102, (2002).
84 F. E.Scalas, R.Gorenflo, Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation, Phys.Rev.E. 69, 011107, (2004).
85 R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi, Disrete random walk models for space-time fractional diffusion, Chem.Phys. 284, 521, (2002).
86 G. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Phys.Rep. 371, 461, (2002).