The evolution equation for the radius of a premixed flame ball in fractional diffusive media

European Physical Journal: Special Topics

Volumn 193, Issue 1, 2011, Pages 105-117

  Pagnini, G ^a  

^a CRS4 ^*  (Italy)

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EID: 79953716826     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2011-01385-3     Document Type: Article

References (34)

1. Ya. B. Zeldovich, Theory of Combustion and Detonation of Gases (USSR Academy of Sciences, Moscow, 1944).
2. P. D. Ronney, Combust. Flame 82, 1 (1990).
3. P. D. Ronney, K. N. Whaling, A. Abbud-Madrid, J. L. Gatto, V. L. Pisowicz, AIAA J. 32, 569 (1994).
4. P. D. Ronney, M. S. Wu, H. G. Pearlman, K. J. Weiland, AIAA J. 36, 1361 (1998).
5. G. Joulin, Combust. Sci. Tech. 185, 99 (1985).
6. J. D. Buckmaster, G. Joulin, P. D. Ronney, Combust. Flame 79, 381 (1990).
7. J. D. Buckmaster, G. Joulin, P. D. Ronney, Combust. Flame 84, 411 (1991).
8. V. Guyonne, P. Noble, J. SIAM Appl. Math. 67, 854 (2007).
9. G. Pagnini, in Proceedings of FDA10. The 4th IFAC Workshop Fractional Differentiation and its Applications, edited by I. Podlubny, B. M. Vinagre Jara, YQ. Chen, V. Feliu Batlle, I. Tejado Balsera (ISBN 9788055304878, 2010), Article no. FDA10-063.
10. G. Pagnini, Fract. Calc. Appl. Anal. 14, 80 (2011).
11. J. Klafter, I. M. Sokolov, Physics World August, 29 (2005).
12. I. M. Sokolov, J. Klafter, A. Blumen, Physics Today November, 48 (2002).
13. A. Mura, M. S. Taqqu, F. Mainardi, Physica A 387, 5033 (2008) http://arxiv. org/abs/0712. 0240.
14. A. Mura, G. Pagnini, J. Phys. A 41, 285003 (2008) http://arxiv. org/abs/0801. 4879.
15. F. Mainardi, G. Pagnini, Fract. Calc. Appl. Anal. 4, 153 (2011).
16. R. Gorenflo, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics, edited by edfnA. Carpinteri, F. Mainardi (Springer-Verlag, Wien and New York, 1997), p. 223, http://arxiv. org/abs/0805. 3823.
17. C. P. Li, Z. G. Zhao, Eur. Phys. J. Special Topics 193, 5 (2011).
18. J. Audounet, J.-M. Roquejoffre, in ESAIM: Proceedings Fractional Differential Systems: Models, Methods and Applications, edited by D. Matignon G. Montseny, Vol. 5 (SMAI, Paris, 1998), p. 15, http://www. emath. fr/proc/vol. 5/.
19. J. Audounet, J.-M. Roquejoffre, H. Rouzaud, Math. Modelling Numer. Anal. 36, 273 (2002).
20. F. Dubois, S. Mengué, Numerical Algorithms 34, 303 (2003).
21. K. Diethelm, M. Weilbeer, Fract. Calc. Appl. Anal. 7, 1 (2004).
22. A. Mura, Ph. D. thesis, University of Bologna, 2008 http://www. fracalmo. org/Mura/.
23. F. Mainardi, Chaos, Solitons Fractals 7, 1461 (1996).
24. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
25. F. Mainardi, A. Mura, G. Pagnini, Int. J. Diff. Equations 2010, 104505 (2010) http://www. hindawi. com/journals/ijde/2010/104505. html.
26. V. Kiryakova, Generalized Fractional Calculus and Applications (Longman, Harlow, 1994).
27. A. Mura, F. Mainardi, Integral Transforms Spec. Funct. 20, 185 (2009) http://arxiv. org/abs/0711. 0665.
28. E. K. Lenzi, M. K. Lenzi, L. R. Evangelista, L. C. Malacarne, R. S. Mendes, J. Stat. Mech., P02048 (2009).
29. J. Audounet, V. Giovangigli, J.-M. Roquejoffre, Physica D 121, 295 (1998).
30. H. Rouzaud, C. R. Acad. Sci. Paris Série I 332, 1083 (2001).
31. R. Gorenflo, S. Vessella, Abel Integral Equations. Analysis and Applications (Springer-Verlag, Berlin, 1991).
32. H. Rouzaud, Revista Matem. Compl. 16, 207 (2003).
33. J.-M. Roquejoffre, H. Rouzaud, J. Comput. Appl. Math. 190, 376 (2006).
34. C. Lederman, J.-M. Roquejoffre, N. Wolanski, C. R. Acad. Sci. Paris Série I 334, 569 (2002).