January 2001  010103
Fractional diffusion processes: recent papers by "fracalmo"
promoters
The are so many papers on fractional diffusion processes published
in several journals (mathematics, physics, engineering, finance,...)
that any list of references on the subject is far to be exhaustive.
Furthermore, the number of papers is growing so quickly that an update
bibliography is (almost) impossible. This interest is increasing in
spite of several people who do not trust in the physical and/or mathematical
relevance of fractional calculus!
Here we would like to present a preliminary list of
recent references related to our approach to fractional diffusion, based
upon the Caputo fractional derivative for time and the RieszFeller
fractional derivative for space. The authors of these papers are thus
the promoters of this WEB site and their associates. We shall refer
to papers of other authors in future NEWS; in a next news we shall refer
to recent papers by Professor M. Caputo.
We divide our papers (some of which already downloadable, others soon)
in 3 groups:
1) Generalities and solutions for fractional diffusion equations
2) Random walk models for fractional diffusion
3) Applications to continuoustime finance
1) Generalities and solutions for fractional diffusion equations
P. Paradisi, R. Cesari, F. Mainardi and F. Tampieri (2001):
The fractional Fick's law for nonlocal transport processes,
Physica A, Vol. 293, No 12, 130142 (2001)
F. Mainardi, Yu Luchko and G. Pagnini (2001):
The fundamental solutions of the spacetime fractional diffusion equation,
Fractional Calculus and Applied Analysis, Vol. 4, No 2 (2001), pp 153192.
[Paper dedicated to Professor Rudolf Gorenflo for his 70th
birthday]
[preprint downloadable]
R. Gorenflo, Yu. Luchko and F. Mainardi (2000):
Wright functions as scaleinvariant solutions of the diffusionwave
equation,
J. Computational and Appl. Mathematics, Vol. 118 No 12, 175191 (2000).
F. Mainardi and F. Tampieri (1999):
Diffusion regimes in Brownian motion induced by the Basset history force,
Technical Report No 1 (ISAOTP99/1), ISAOCNR, Bologna, March 1999,
pp. 24.
[Invited Lecture, Meeting of the TAO Working Group on Diffusion, Stockholm,
Sweden, 611 October 1997]
R. Gorenflo and F. Mainardi (1999):
Feller fractional diffusion and Levy stable motions,
Mini Proceedings of the International Conference on "Levy Processes:
Theory and Applications", MaPhySto (Mathematical Physics and Stochastics
Centre), Department of Mathematics, University of Aarhus, Denmark 1822
January 1999. MPSmisc. 199911, April 1999, pp. 11122, edited by O.E.
BarndorffNielsen, S.E. Graversen and T. Mikosch.
[preprint downloadable]
R. Gorenflo and F. Mainardi (1998):
Signalling problem and DirichletNeumann map for timefractional diffusionwave
equations,
Matimyas Matematika, Vol. 21, August 1998, pp. 109118.
[Special issue of Matimyas Matematika (Official Journal of the Mathematical
Society of the Philippines) edited by R. Gorenflo and M. P. Navarro,
Proceedings of the International Conference on "Inverse Problems and
Applications", University of the Philippines  Diliman, February 2327,
1998, ISSN 01156926]
Preprint No. A07/98, Freie Universitat Berlin, Serie A Mathematik (1998).
[http://www.math.fuberlin.de/publ]
R. Gorenflo and F. Mainardi :
Fractional calculus and stable probability distributions,
Archives of Mechanics, Vol. 50 (3), 377388 (1998).
[preprint downloadable]
F. Mainardi, P. Paradisi and R. Gorenflo (1997):
Probability distributions generated by fractional diffusion equations,
to appear in J. Kertesz and I. Kondor (Editors), "Econophysics: an Emerging
Science", Kluwer, Dordrecht ????, pp. 39.
[Invited Lecture, Workshop on Econophysics, Budapest 2127 July 1997]
[preprint downloadable]
F. Mainardi and M. Tomirotti (1997):
Seismic pulse propagation with constant Q and stable probability distributions,
Annali Geofisica, Vol. 40, 13111328 (1997).
[Paper dedicated to Professor Michele CAPUTO for his 70th birthday]
F. Mainardi (1997):
Fractional Calculus, Some Basic Problems in Continuum and Statistical
Mechanics,
in A. Carpinteri and F. Mainardi (Editors), "Fractals and Fractional
Calculus in Continuum Mechanics", Springer Verlag, Wien and New York
(1997), pp. 291348.
[Vol. no 378, series CISM Courses and Lecture Notes, ISBN 321182913X]
[Lecture Notes of the Advanced School held at CISM, Udine, Italy, 2327
September 1996]
2) Random walk models for fractional diffusion
R. Gorenflo, P. Paradisi, F. Mainardi and D. Moretti (2001)
Random walk models for spacetime fractional diffusion,
Preprint, to appear.
R. Gorenflo and F. Mainardi (2000):
Random walk models approximating symmetric spacefractional diffusion
processes,
in: J. Elschner, I. Gohberg and B. Silbermann (Editors), Problems
in Mathematical Physics (Siegfried Prossdorf Memorial Volume). Proceedings
of the 11th TMP Conference. (Birkhauser Verlag, BostonBaselBerlin,
2000), pp. 120145
R. Gorenflo and F. Mainardi (2000):
Approximation of LevyFeller diffusion by random walk,
J. Analysis and its Applications (ZAA), Vol. 18 (2), 231246 (1999).
[preprint downloadable]
R. Gorenflo, G. De Fabritiis and F. Mainardi (1999):
Discrete random walk models for symmetric LevyFeller diffusion processes,
Physica A, Vol. 269 (1) 7989 (1999).
[preprint downloadable
or at http://xxx.lanl.gov/abs/condmat/9903264]
[Special issue of Physica A, edited by R.N. Mantegna, containing the
Proceedings of the International Workshop on "Econophysics and Statistical
Finance", Palermo (Italy), 2830 September 1998]
R. Gorenflo and F. Mainardi (1998):
Random walk models for spacefractional diffusion processes,
Fractional Calculus and Applied Analysis, Vol. 1 (2), 167191 (1998).
[preprint downloadable]
3) Applications in ContinuousTime Finance
R. Gorenflo, F. Mainardi, M. Raberto and E. Scalas :
Fractional diffusion in finance: basic theory,
in G.I. Bischi and L. Gardini (Editors), Proceedings of the Workshop
Modelli Dinamici in Economia e Finanza (MDEF2000), Urbino, September
2830, 2000. [www.econ.uniurb.it/bischi/mdef2000.htm]
R. Gorenflo, F. Mainardi, E. Scalas and M. Raberto (2000):
Fractional calculus and continuoustime finance III: the diffusion limit,
Preprint, to appear.
F. Mainardi, M. Raberto, R. Gorenflo and E. Scalas (2000):
Fractional calculus and continuoustime finance II: the waitingtime
distribution,
Physica A, Vol. 287, No 34, 468481 (2000).
[http://xxx.lanl.gov/abs/condmat/0006454]
[Special issue of Physica A, edited by F. Schweitzer and D. Helbing,
containing the Proceedings of the International Workshop on "Economic
Dynamics from the Physics Point of View", BadHonnef (Germany), 2730
March 2000]
E. Scalas, R. Gorenflo and F. Mainardi :
Fractional calculus and continuoustime finance,
Physica A, Vol. 284, No 14, 376384 (2000)
[Preprint downloadable from http://xxx.lanl.gov/abs/condmat/0001120]
