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References
| 1. |
Baeumer, Boris; Meerschaert, Mark M. Stochastic solutions for fractional Cauchy problems. Fract. Calc. Appl. Anal. 4 (2001), no. 4, 481--500. MR1874479 (2003d:26006) |
| 2. |
Baeumer, Boris; Meerschaert, Mark M.; Nane, Erkan. Space-time duality for fractional diffusion. J. Appl. Probab. 46 (2009), no. 4, 1100--1115. MR2582709 (Review) |
| 3. |
Beghin, Luisa; Orsingher, Enzo. The telegraph process stopped at stable-distributed times and its connection with the fractional telegraph equation. Fract. Calc. Appl. Anal. 6 (2003), no. 2, 187--204. MR2035414 (2004m:60087) |
| 4. |
Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564 (98e:60117) |
| 5. |
Bondesson, Lennart; Kristiansen, Gundorph K.; Steutel, Fred W. Infinite divisibility of random variables and their integer parts. Statist. Probab. Lett. 28 (1996), no. 3, 271--278. MR1407001 (97f:60037) |
| 6. |
DeBlassie, R. Dante. Higher order PDEs and symmetric stable processes. Probab. Theory Related Fields 129 (2004), no. 4, 495--536. MR2078980 (2005d:60079) |
| 7. |
D'Ovidio, Mikro; Orsingher, Enzo Composition of processes and related partial differential equations. J. Theor. Probab. (published on line) (2010) |
| 8. |
D'Ovidio, Mirko; Orsingher, Enzo Bessel processes and hyperbolic Brownian motions stopped at different random times.Under revision for Stochastic Processes and their Applications (arXiv:1003.6085v1) (2010) |
| 9. |
Feller, William An introduction to probability theory and its applications. volume 2. 2nd edition, (1971) |
| 10. |
Fox, Charles. The $G$ and $H$ functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98 1961 395--429. MR0131578 (24 #A1427) |
| 11. |
Gorenflo, Rudolf; Mainardi, Francesco Fractional calculus: integral and differential equations of frational order in A. Carpinteri and F. Mainardi (Editors). Fractals and Fractional Calculus in Continuum Mechanics. Wien and New York, Springher Verlag, 223 - 276, (1997) |
| 12. |
Gradshteyn, I. S.; Ryzhik, I. M. Table of integrals, series, and products. Translated from the Russian.Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger.With one CD-ROM (Windows, Macintosh and UNIX). Seventh edition. Elsevier/Academic Press, Amsterdam, 2007. xlviii+1171 pp. ISBN: 978-0-12-373637-6; 0-12-373637-4 MR2360010 (2008g:00005) |
| 13. |
Kilbas, Anatoly A.; Srivastava, Hari M.; Trujillo, Juan J. Theory and applications of fractional differential equations (North-Holland Mathematics Studies), volume 204. Elsevier, Amsterdam, (2006) |
| 14. |
Kochubeĭ, A. N. The Cauchy problem for evolution equations of fractional order. (Russian) Differentsialʹnye Uravneniya 25 (1989), no. 8, 1359--1368, 1468; translation in Differential Equations 25 (1989), no. 8, 967--974 (1990) MR1014153 (90g:34063) |
| 15. |
Kochubeĭ, A. N. Diffusion of fractional order. (Russian) Differentsialʹnye Uravneniya 26 (1990), no. 4, 660--670, 733--734; translation in Differential Equations 26 (1990), no. 4, 485--492 MR1061448 (91j:35133) |
| 16. |
Kotz, Samuel; Balakrishnan, N.; Johnson, Norman L. Continuous multivariate distributions. Vol. 1. Models and applications. Second edition. Wiley Series in Probability and Statistics: Applied Probability and Statistics. Wiley-Interscience, New York, 2000. xxii+722 pp. ISBN: 0-471-18387-3 MR1788152 (2001h:62001) |
| 17. |
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001), no. 2, 153--192. MR1829592 (2002h:26010) |
| 18. |
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf. Mellin transform and subordination laws in fractional diffusion processes. Fract. Calc. Appl. Anal. 6 (2003), no. 4, 441--459. MR2044309 (2005a:60058) |
| 19. |
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf. Some aspects of fractional diffusion equations of single and distributed order. Appl. Math. Comput. 187 (2007), no. 1, 295--305. MR2323582 |
| 20. |
Mathai, Arakaparampil M.; Saxena, Ram K. Generalized Hypergeometric functions with applications in statistics and physical sciences.Lecture Notes in Mathematics, n. 348, (1973) |
| 21. |
Meerschaert, Mark M.; Scheffler, Hans-Peter. Triangular array limits for continuous time random walks. Stochastic Process. Appl. 118 (2008), no. 9, 1606--1633. MR2442372 (2010b:60135) |
| 22. |
Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P. Fractional Cauchy problems on bounded domains. Ann. Probab. 37 (2009), no. 3, 979--1007. MR2537547 (2010h:60121) |
| 23. |
Nane, Erkan. Higher order PDE's and iterated processes. Trans. Amer. Math. Soc. 360 (2008), no. 5, 2681--2692. MR2373329 (2008j:60202) |
| 24. |
Nane, Erkan Fractional cauchy problems on bounded domains: survey of recent results. arXiv:1004.1577v1, (2010) |
| 25. |
Nigmatullin, The realization of the generalized transfer in a medium with fractal geometry.Phys. Status Solidi B 133, 425 -- 430, (1986) |
| 26. |
Orsingher, Enzo; Beghin, Luisa. Time-fractional telegraph equations and telegraph processes with Brownian time. Probab. Theory Related Fields 128 (2004), no. 1, 141--160. MR2027298 (2005a:60056) |
| 27. |
Orsingher, Enzo; Beghin, Luisa. Fractional diffusion equations and processes with randomly varying time. Ann. Probab. 37 (2009), no. 1, 206--249. MR2489164 (2010b:60116) |
| 28. |
Samko, Stefan G.; Kilbas, Anatoly A.; Marichev, Oleg I. Fractional integrals and derivatives. Theory and applications. Edited and with a foreword by S. M. Nikolʹskiĭ. Translated from the 1987 Russian original. Revised by the authors. Gordon and Breach Science Publishers, Yverdon, 1993. xxxvi+976 pp. ISBN: 2-88124-864-0 MR1347689 (96d:26012) |
| 29. |
Schneider, W. R.; Wyss, W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989), no. 1, 134--144. MR0974464 (89m:45017) |
| 30. |
Wyss, Walter. The fractional diffusion equation. J. Math. Phys. 27 (1986), no. 11, 2782--2785. MR0861345 (87m:44008) |
| 31. |
Zaslavsky, G. M. Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion (Gavi, 1993). Phys. D 76 (1994), no. 1-3, 110--122. MR1295881 (95h:58120) |
| 32. |
Zolotarev, V. M. One-dimensional stable distributions. Translated from the Russian by H. H. McFaden. Translation edited by Ben Silver. Translations of Mathematical Monographs, 65. American Mathematical Society, Providence, RI, 1986. x+284 pp. ISBN: 0-8218-4519-5 MR0854867 (87k:60002) |
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