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Zbl 1153.35347
Hanyga, Andrzej
Multidimensional solutions of time-fractional diffusion-wave equations. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2020, 933-957 (2002). ISSN 1364-5021; ISSN 1471-2946/e

Summary: Green's functions and propagator functions for the time-fractional generalized diffusion-wave equation in one and three dimensions are expressed in terms of Wright functions. In two dimensions they are expressed in terms of an integral involving the Macdonald function. Their properties are studied analytically and numerically.

MSC 2000:: *35K57 Reaction-diffusion equations
35A08 Fundamental solutions of PDE
35B30 Dependence of solutions of PDE on initial and boundary data

Keywords: diffusion; $Q$ factor; fractional calculus; stable probability distributions

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