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Multi-dimensional solutions of space-time-fractional diffusion equations. (English) Zbl 0999.60035
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.
60G18Self-similar processes
60J60Diffusion processes
45K05Integro-partial differential equations