Some recent advances in theory and simulation of fractional diffusion processes

Authors:
Rudolf Gorenflo;Francesco Mainardi
Affiliations:
Department of Mathematics and Informatics, Free University of Berlin, Arnimallee 3, D-14195 Berlin, Germany;Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

To offer an insight into the rapidly developing theory of fractional diffusion processes, we describe in some detail three topics of current interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag-Leffler waiting time law in time-fractional processes, (iii) our method of parametric subordination for generating particle trajectories.