1 | R. Bagley and P. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheology 27 (1983), 201–210. |
2 | S. Bochner, Harmonic Analysis and the Theory of Probability. University of California Press, Berkeley (1955). |
3 | J. Cushman and M. Moroni, Statistical mechanics with three-dimensional particle tracking velocimetry in the study of anomalous dispersion, I: Theory. Phys. Fluids 13 (2001), 75–80. |
4 | D. del-Castillo-Negrete, Fractional diffusion models of anomalous transport. In: R. Klages, G. Radons, and I. Sokolov (Eds.), Anomalous Transport: Foundations and Applications. Wiley-VCH, Weinheim (2008), 163–212. |
5 | M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes. DeGruyter, Berlin, 2nd Ed. (2011). |
6 | R. Haag, Local Quantum Physics. Springer Verlag, Berlin (1992). |
7 | R. Hilfer, Classification theory for anequilibrium phase transitions. Phys. Rev. E 48 (1993), 2466–2475. |
8 | R. Hilfer, Foundations of fractional dynamics. Fractals 3 (1995), 549–556. |
9 | R. Hilfer, On fractional diffusion and its relation with continuous time random walks. In: A. P. R. Kutner and K. Sznajd-Weron (Eds.), Anomalous Diffusion: From Basis to Applications. Springer, Berlin (1999), 77–82. |
10 | R. Hilfer, Applications of Fractional Calculus in Physics. World Scientific Publ. Co., Singapore (2000). |
11 | R. Hilfer, Fractional time evolution. In: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000), 87–130. |
12 | R. Hilfer, Threefold introduction to fractional derivatives. In: R. Klages, G. Radons, and I. Sokolov (Eds.), Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim (2008), 17–74. |
13 | R. Hilfer and L. Anton, Fractional master equations and fractal time random walks. Phys. Rev. E, Rapid Commun. 51 (1995), R848–R851. |
14 | J. Klafter, S.C. Lim, R. Metzler (Eds.), Fractional Dynamics. Recent Advances. World Scientific, Singapore (2011). |
15 | R. Klages G. Radons, and I. Sokolov (Eds.), Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim (2008). |
16 | N. Landkof, Foundations of Modern Potential Theory. Springer, Berlin (1972). |
17 | N. Laskin, Principles of fractional quantum mechanics. In: R. Klages, G. Radons, and I. Sokolov (Eds.), Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim (2008), 393–427; DOI: 10.1142/97898143405950017. |
18 | P. Levy, Theorie de l’addition des variables aleatoires. Gauthier-Villars, Paris (1937). |
19 | J. Liouville, Mémoire sur quelques questions de geometrie et de mecanique, et sur un nouveau genre de calcul pour resoudre ces questions. Journal de l’Ecole Polytechnique XIII (1832), 1–69. |
20 | E. Montroll and G. Weiss, Random walks on lattices, II. J. Math. Phys. 6 (1965), 167–181. |
21 | R. Nigmatullin. The realization of the generalized transfer equation in a medium with fractal geometry. Phys. Stat. Sol. B 133 (1986), 425–430. |
22 | M. Riesz, Integrales de Riemann-Liouville et potentiels. Acta Sci. Math. (Szeged) 9 (1938), 1–42. |
23 | M. Riesz, L’integrale de Riemann-Liouville et le probleme de Cauchy. Acta Mathematica 81 (1949), 1–222. |
24 | Y. Rossikhin and M. Shitikova. Application of fractional calculus for analysis of nonlinear damped vibrations of suspension bridges. J. Eng. Mech. 124 (1998), 1029–1036. |
25 | I. Schäfer and K. Krüger. Modelling of coils using fractional derivatives. J. of Magnetism and Magnetic Materials 307 (2006), 91–98. |
26 | W. Schneider and W. Wyss, Fractional diffusion and wave equations. J. Math. Phys. 30 (1989), 134–144. |
27 | R. Schumer, D. Benson, M. Meerschaert, and S. Wheatcraft, Eulerian derivation of the fractional advection-dispersion equation. J. Contaminant Hydrol. 48 (2001), 69–86. |
28 | V. Uchaikin, Fractional Derivatives for Physicists and Engineers, I. Springer, Berlin (2012). |
29 | V. Uchaikin, Fractional Derivatives for Physicists and Engineers, II. Springer, Berlin (2013). |