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1 G.W. Scott-Blair and J.E. Caffyn. An application of the theory of quasi-properties to the treatment of anomalous stress-strain relations. Phil. Mag., 40:80, 1949.
2 H. Berens and U. Westphal. A Cauchy problem for a generalized wave equation. Acta Sci. Math. (Szeged), 29:93, 1968.
3 K.B. Oldham and J.S. Spanier. The replacement of Fick’s law by a formulation involving semidifferentiation. J. Electroanal. Chem. Interfacial Electrochem., 26:331, 1970.
4 M. Caputo and F. Mainardi. Linear models of dissipation in anelastic solids. Riv.Nuovo Cim., 1:161, 1971.
5 K.B. Oldham and J.S. Spanier. The Fractional Calculus. Academic Press, New York, 1974.
6 R. Hilfer. Classification theory for anequilibrium phase transitions. Phys. Rev. E, 48:2466, 1993.
7 R. Hilfer. On a new class of phase transitions. In W.P. Beyermann, N.L. Huang-Liu, and D.E. MacLaughlin, editors, Random Magnetism and High-Temperature Superconductivity, page 85, Singapore,, 1994. World Scientific Publ. Co.
8 R. Hilfer. Exact solutions for a class of fractal time random walks. Fractals, 3(1):211, 1995.
9 R. Hilfer. Fractional dynamics, irreversibility and ergodicity breaking. Chaos, Solitons & Fractals, 5:1475, 1995.
10 R. Hilfer. Foundations of fractional dynamics. Fractals, 3:549, 1995.
11 R. Hilfer. An extension of the dynamical foundation for the statistical equilibrium concept. Physica A, 221:89, 1995.
12 R.L. Bagley and P.J. Torvik. A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheology, 27:201, 1983.
13 R.L. Bagley and P.J. Torvik. On the fractional calculus model of viscoelastic behaviour. J. Rheology, 30:133, 1986.
14 W. Wyss. The fractional diffusion equation. J. Math. Phys., 27:2782, 1986.
15 W.R. Schneider and W. Wyss. Fractional diffusion and wave equations. J. Math. Phys., 30:134, 1989.
16 A.M.A. El-Sayed. Fractional-order diffusion-wave equation. Int. J. Theor. Phys., 35:311, 1996.
17 A. Compte. Stochastic foundations of fractional dynamics. Phys.Rev. E, 55:4191, 1996.
18 T.F. Nonnenmacher and W.G. Glöckle. A fractional model for mechanical stress relaxation. Phil. Mag. Lett., 64:89, 1991.
19 L. Gaul, P. Klein, and S. Kempfle. Damping description involving fractional operators. Mechanical Systems and Signal Processing, 5:81, 1991.
20 H. Beyer and S. Kempfle. Definition of physically consistent damping laws with fractional derivatives. A. angew. Math. Mech., 75:623, 1995.
21 R.R. Nigmatullin. The realization of the generalized transfer equation in a medium with fractal geometry. phys. stat. sol. b, 133:425, 1986.
22 S. Westlund. Dead matter has memory ! Physica Scripta, 43:174, 1991.
23G. Jumarie. A Fokker-Planck equation of fractional order with respect to time. J. Math. Phys., 33:3536, 1992.
24 H. Schiessel and A. Blumen. Fractal aspects in polymer science. Fractals, 3:483, 1995.
25 G. Zaslavsky. Fractional kinetic equation for Hamiltonian chaos. Physica D, 76:110, 1994.
26 G. Zaslavsky. From Hamiltonian chaos to Maxwell’s demon. Chaos, 5:653, 1995.
27 E. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton, 1971.
28 C. Berg and G. Forst. Potential Theory on Locally Compact Abelian Groups. Springer, Berlin, 1975.
29 A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev. Integrals and Series, volume 4. Gordon and Breach, New York, 1992.
30 B.V. Gnedenko and A.N. Kolmogorov. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Cambridge, 1954.
31 W. Feller. An Introduction to Probability Theory and Its Applications, volume II. Wiley, New York, 1971.
32 F. Oberhettinger. Tables of Mellin Transforms. Springer Verlag, Berlin, 1974.
33 I.A. Ibragimov and Yu.V. Linnik. Independent and Stationary Sequences of Random Variables. Wolters-Nordhoff Publishing, Groningen, 1971.
34 S. Bochner. Harmonic Analysis and the Theory of Probability. University of California Press, Berkeley, 1955.
35 K. Yosida. Functional Analysis. Springer, Berlin, 1965.
36 A.V. Balakrishnan. Fractional powers of closed operators and the semigroups generated by them. Pacific J. Math., 10:419, 1960.
37 U. Westphal. Ein Kalkül für gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren. Compositio Math., 22:67, 1970.
38 L. Bieberbach. Lehrbuch der Funktionentheorie, volume II. Teubner, Leipzig, 1931.
39 W.R. Schneider. Completely monotone generalized Mittag-Leffler functions. Expo. Math., 14:3, 1996.
40 P.L. Butzer and R. J. Nessel. Fourier Analysis and Approximation, volume 1. Birkhäuser Verlag, Basel, 1971.
41 R. Hilfer and L. Anton. Fractional master equations and fractal time random walks. Phys.Rev.E, Rapid Commun., 51:848, 1995.
42 R. Hilfer. On fractional diffusion and its relation with continuous time random walks. In A. Pekalski R. Kutner and K. Sznajd-Weron, editors, Anomalous Diffusion: From Basis to Applications, page 77. Springer, 1999.
43 E.W. Montroll and G.H. Weiss. Random walks on lattices II. J. Math. Phys., 6:167, 1965.
44 M.N. Barber and B.W. Ninham. Random and Restricted Walks. Gordon and Breach Science Publ., New York, 1970.
45 J.W. Haus and K. Kehr. Diffusion in regular and disordered lattices. Phys.Rep., 150:263, 1987.
46 J. Klafter, A. Blumen, and M.F. Shlesinger. Stochastic pathway to anomalous diffusion. Phys. Rev. A, 35:3081, 1987.
47 B.D. Hughes. Random Walks and Random Environments, volume 1. Clarendon Press, Oxford, 1995.
48 B.D. Hughes. Random Walks and Random Environments, volume 2. Clarendon Press, Oxford, 1996.
49 J.K.E. Tunaley. Some properties of the asymptotic solutions of the Montroll-Weiss equation. J. Stat. Phys., 12:1, 1975.
50 E.W. Montroll and B.J. West. On an enriched collection of stochastic processes. In E.W. Montroll and J.L Lebowitz, editors, Fluctuation Phenomena, page 61, Amsterdam, 1979. North Holland Publ. Co.
51 G.H. Weiss and R.J. Rubin. Random walks: Theory and selected applications. Adv. Chem. Phys., 52:363, 1983.
52 A. Erdelyi (et al.). Higher Transcendental Functions, volume III. Mc Graw Hill Book Co., New York, 1955.
53 M.F. Shlesinger. Asymptotic solutions of continuous time random walks. J. Stat. Phys., 10:421, 1974.
54 M.F. Shlesinger, J. Klafter, and Y.M. Wong. Random walks with infinite spatial and temporal moments. J. Stat. Phys., 27:499, 1982.
55 C. Fox. The G and H functions as symmetrical Fourier kernels. Trans. Am. Math. Soc., 98:395, 1961.
56 B.L.J. Braaksma. Asymptotic expansions and anlytic continuations for a class of Barnes-integrals. Compos.Math., 15:239, 1964.
57 A.M. Mathai and R.K. Saxena. The H-function with Applications in Statistics and Other Disciplines. Wiley, New Delhi, 1978.
58 H.M. Srivastava, K.C. Gupta, and S.P. Goyal. The H-functions of One and Two Variables with Applications. South Asian Publishers, New Delhi, 1982.
59 A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev. Integrals and Series, volume 3. Gordon and Breach, New York, 1990.
60 I.N. Sneddon. The Use of Integral Transforms. Mc Graw Hill, New York, 1972.