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Zbl 0999.60035
Hanyga, Andrzej
Multi-dimensional solutions of space-time-fractional diffusion equations. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No.2018, 429-450 (2002). ISSN 1364-5021; ISSN 1471-2946/e

The author investigates multi-dimensional isotropic and non-isotropic diffusion processes fractional both in space and time. He gives integral representations for the Green functions and the propagators, then pays special attention to questions of uniqueness and well-posedness. Furthermore he discusses the transition to wave propagation for the case of the order of the frational time-derivative being greater than 1. In detail and on a high mathematical level the following topics are treated: Space-time fractional diffusion with central symmetry, spherically symmetric space-time fractional equations, well-posedness, unimodality of the propagator and Green's function, moments of the propagator, wave propagation, numerical solutions. He concludes his paper with 38 valuable references.
[Rudolf Gorenflo (Berlin)]

MSC 2000:: *60G18 Self-similar processes
60J60 Diffusion processes
45K05 Integro-partial differential equations

Keywords: anomalous diffusion; fractional calculus; unimodality; anisotropic multi-dimensional problems

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Zentralblatt MATH Berlin [Germany]