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All issues Volume 11 / No 3 (2016) Math. Model. Nat. Phenom., 11 3 (2016) 1-17 References
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Issue
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
Page(s) 1 - 17
DOI https://doi.org/10.1051/mmnp/201611301
Published online 21 June 2016
  1. G. Germano, M. Politi, E. Scalas, R.L. Schilling. Stochastic calculus for uncoupled continuous-time random walks. Physical Review E, 79 (2009), 066102. [CrossRef] [Google Scholar]
  2. R. Gorenflo. Stochastic processes related to time-fractional diffusion-wave equation. Communications in Applied and Industrial Mathematics, 6 (2014), e-531. [Google Scholar]
  3. R. Gorenflo, F. Mainardi. Subordination Pathways to Fractional Diffusion. Eur. Phys. J. Special Topics, 193 (2011), 119–132. [CrossRef] [EDP Sciences] [Google Scholar]
  4. R. Gorenflo, J. Loutchko, Yu. Luchko. Computation of the Mittag-Leffler function and its derivatives. Fract. Calc. Appl. Anal., 5 (2002), 491–518. [MathSciNet] [Google Scholar]
  5. R. Gorenflo, A.A. Kilbas, F. Mainardi, S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications. Springer, Berlin, 2014. [Google Scholar]
  6. A. Hanyga. Multi-dimensional solutions of space-time-fractional diffusion equations. Proc. R. Soc. London. A, 458 (2002), 429–450. [CrossRef] [Google Scholar]
  7. R. Hilfer, L. Anton. Fractional master equations and fractal time random walks. Phys. Rev. E, Rapid Commun., 51 (1995), R848. [CrossRef] [Google Scholar]
  8. K.H. Hoffmann, C. Essex, C. Schulzky. Fractional diffusion and entropy production. J. Non-Equilib. Thermodyn., 23 (1998), 166–175. [CrossRef] [Google Scholar]
  9. M. Kenkre, E.W. Montroll, M.F. Shlesinger. Generalized master equations for continuous-time random walks. Journal of Statistical Physics, 9 (1973), 45–50. [CrossRef] [Google Scholar]
  10. R. Klages, G. Radons, I.M. Sokolov. Anomalous Transport: Foundations and Applications. Wiley-VCH, 2008. [Google Scholar]
  11. X. Li, C. Essex, M. Davison, K.H. Hoffmann, C. Schulzky. Fractional diffusion, irreversibility and entropy. J. Non-Equilib. Thermodyn., 28 (2003), 279–291. [Google Scholar]
  12. Yu. Luchko. Entropy production rate of a one-dimensional alpha-fractional diffusion process. Axioms, 5 (2016), doi:10.3390/axioms5010006. [CrossRef] [Google Scholar]
  13. Yu. Luchko. Wave-diffusion dualism of the neutral-fractional processes. Journal of Computational Physics, 293 (2015), 40–52. [Google Scholar]
  14. Yu. Luchko. Multi-dimensional fractional wave equation and some properties of its fundamental solution. Communications in Applied and Industrial Mathematics, 6 (2014), e-485. [CrossRef] [Google Scholar]
  15. Yu. Luchko. Fractional wave equation and damped waves. J. Math. Phys., 54 (2013), 031505. [CrossRef] [Google Scholar]
  16. Yu. Luchko. Models of the neutral-fractional anomalous diffusion and their analysis. AIP Conf. Proc., 1493 (2012), 626–632. [CrossRef] [Google Scholar]
  17. Yu. Luchko. Anomalous diffusion models and their analysis. Forum der Berliner mathematischen Gesellschaft, 19 (2011), 53–85. [Google Scholar]
  18. Yu. Luchko, R. Gorenflo. An operational method for solving fractional differential equations with the Caputo derivatives. Acta Mathematica Vietnamica, 24 (1999), 207–233. [Google Scholar]
  19. Yu. Luchko, V. Kiryakova. The Mellin integral transform in fractional calculus. Fract. Calc. Appl. Anal., 16 (2013), 405–430. [CrossRef] [Google Scholar]
  20. M. Magdziarz, A. Weron, J. Klafter. Equivalence of the Fractional Fokker-Planck and Subordinated Langevin Equations: The Case of a Time-Dependent Force. Phys. Rev. Lett., 101 (2008), 210601. [CrossRef] [PubMed] [Google Scholar]
  21. F. Mainardi, Yu. Luchko, G. Pagnini. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal., 4 (2001), 153–192. [MathSciNet] [Google Scholar]
  22. O.I. Marichev. Handbook of Integral Transforms of Higher Transcendental Functions. Theory and Algorithmic Tables. Ellis Horwood, 1983. [Google Scholar]
  23. R. Metzler, J.-H. Jeon, A.G. Cherstvy, E. Barkai. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys. Chem. Chem. Phys., 16 (2014), 24128–24164. [CrossRef] [PubMed] [Google Scholar]
  24. R. Metzler, J. Klafter. The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A. Math. Gen., 37 (2004), R161–R208. [Google Scholar]
  25. R. Metzler, J. Klafter. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339 (2000), 1–77. [Google Scholar]
  26. A. Mura, G. Pagnini. Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor., 41 (2008), 285003. [CrossRef] [MathSciNet] [Google Scholar]
  27. G. Pagnini. Short note on the emergence of fractional kinetics. Physica A, 409 (2014), 29–34. [CrossRef] [Google Scholar]
  28. G. Pagnini. Erdélyi-Kober fractional diffusion. Fract. Calc. Appl. Anal., 15 (2012), 117–127. [CrossRef] [Google Scholar]
  29. Yu. Povstenko. Linear Fractional Diffusion-Wave Equation for Scientists and Engineers. Birkhäuser, 2015. [Google Scholar]
  30. J. Prehl, C. Essex, K.H. Hoffmann. The superdiffusion entropy production paradox in the space-fractional case for extended entropies. Physica A, 389 (2010), 214–224. [CrossRef] [Google Scholar]
  31. S.G. Samko, A.A. Kilbas, O.I. Marichev. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, 1993. [Google Scholar]
  32. W.R. Schneider, W. Wyss. Fractional diffusion and wave equations. J. Math. Phys., 30 (1989), 134–144. [CrossRef] [Google Scholar]
  33. S. Umarov. Continuous time random walk models associated with distributed order diffusion equations. Fract. Calc. Appl. Anal., 18 (2015), 821–837. [MathSciNet] [Google Scholar]
  34. Matlab File Exchange, Matlab-Code that calculates the Mittag-Leffler function with desired accuracy, available for download at www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function. [Google Scholar]

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