Royal Society Publishing

Multi–dimensional solutions of space–time–fractional diffusion equations

Andrzej Hanyga

Abstract

Green's functions and propagators for the multi–dimensional anisotropic space–time fractional diffusion equation are obtained in integral form. Uniqueness of the solutions is studied in the framework of abstract Volterra equations. Unimodality of propagator functions is demonstrated in the centrally symmetric case. The transition from diffusion to wave propagation is discussed. Numerical examples are constructed.

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