Subordination pathways to fractional diffusion

European Physical Journal: Special Topics

Volumn 193, Issue 1, 2011, Pages 119-132

  Gorenflo, R ^a   Mainardi, F ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953682830     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2011-01386-2     Document Type: Article

References (30)

1. E. Barkai, Phys. Rev. E 63, 046118-1/18 (2001).
2. P. Butzer, U. Westphal, in Fractional Calculus, Applications in Physics, edited by H. Hilfer (World Scientific, Singapore, 2000), p. 1.
3. W. Feller, An Introduction to Probability Theory and its Applications, Vol. II (Wiley, New York, 1971).
4. H. C. Fogedby, Phys. Rev. E 50, 1657 (1994).
5. D. Fulger, E. Scalas, G. Germano, Phys. Rev. E 77, 021122 (2008).
6. G. Germano, M. Politi, E. Scalas, R. L. Schilling, Phys. Rev. E 79, 066102 (2009).
7. R. Gorenflo, in Proceedings of the National Workshop on Fractional Calculus and Statistical Distributions, edited by S. S. Pai, N. Sebastian, S. S. Nair, D. P. Joseph, D. Kumar (CMS Pala Campus, India, 2010), p. 1 [E-print: http://arxiv. org/abs/1004. 4413].
8. R. Gorenflo, F. Mainardi, in Fractals and Fractional Calculus in Continuum Mechanics, edited by A. Carpinteri, F. Mainardi (Springer Verlag, Wien, 1997), p. 223 [E-print: http://arxiv. org/abs/0805. 3823].
9. R. Gorenflo, F. Mainardi, in Processes with Long Range Correlations, edited by G. Rangarajan, M. Dings (Springer-Verlag, Berlin, 2003), p. 148 [E-print: http://arxiv. org/abs/0709. 3990].
10. R. Gorenflo, F. Mainardi, in Anomalous Transport, Foundations and Applications, edited by R. Klages, G. Radons, I. M. Sokolov (Wiley-VCH Verlag, Weinheim, Germany, 2008), p. 93 [E-print: arXiv: cond-mat/07050797].
11. R. Gorenflo, F. Mainardi, A. Vivoli, Chaos, Solitons and Fractals 34, 87 (2007) [E-print http://arxiv. org/abs/cond-mat/0701126].
12. R. Hilfer, in Anomalous Transport, Foundations and Applications, edited by R. Klages, G. Radons, I. M. Sokolov (Wiley-VCH Verlag, Weinheim, Germany, 2008), p. 17.
13. R. Hilfer, Fractals 3, 211 (1995).
14. R. Hilfer, L. Anton, Phys. Rev. E 51, R848 (1995).
15. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
16. D. Kleinhans, R. Friedrich, Phys. Rev. E 76, 061102 (2007).
17. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity (Imperial College Press, London, 2010).
18. F. Mainardi, Yu. Luchko, G. Pagnini, Fract. Calculus and Appl. Analysis 4, 153 (2001) [E-print: http://arxiv. org/abs/cond-mat/0702419].
19. F. Mainardi, G. Pagnini, R. K. Saxena, J. Computational and Appl. Mathematics 178, 321 (2005).
20. A. M. Mathai, R. K. Saxena, H. J. Haubold, The H-function, Theory and Applications (Springer Verlag, New York, 2010).
21. M. M. Meerschaert, D. A. Benson, H. P. Scheffler, B. Baeumer, Phys. Rev. E 65, 041103/1 (2002).
22. M. M. Meerschaert, H. P. Scheffler, J. Appl. Prob. 41, 623 (2004).
23. R. Metzler, J. Klafter, J. Phys. A. Math. Gen. 37, R161 (2004).
24. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
25. B. Rubin, Fractional Integrals and Potentials (Addison-Wesley & Longman, Harlow, 1996) [Pitman Monographs and Surveys in Pure and Applied Mathematics No. 82].
26. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, New York, 1993).
27. E. Scalas, R. Gorenflo, F. Mainardi, Phys. Rev. E 69, 011107 (2004).
28. Z. Tomovski, R. Hilfer, H. M. Srivastava, Integral Transforms Spec. Funct. 21, 797 (2010).
29. G. H. Weiss, Aspects and Applications of Random Walks (North-Holland, Amsterdam, 1994).
30. Y. Zhang, M. M. Meerschaert, B. Baeumer, Phys. Rev. E. 78, 036705 (2008).