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Zbl 1239.76057
Povstenko, Yuriy Z.
Central symmetric solution to the Neumann problem for a time-fractional diffusion-wave equation in a sphere. (English)
[J] Nonlinear Anal., Real World Appl. 13, No. 3, 1229-1238 (2012). ISSN 1468-1218

Summary: A time-fractional central symmetric diffusion-wave equation is investigated in a sphere. Two types of Neumann boundary condition are considered: the mathematical condition with the prescribed boundary value of the normal derivative and the physical condition with the prescribed boundary value of the matter flux. Several examples of problems are solved using the Laplace integral transform with respect to time and the finite sine-Fourier transform of the special type with respect to the spatial coordinate. Numerical results are illustrated graphically.

MSC 2000:: *76R50 Diffusion
35R11

Keywords: diffusion-wave equation; non-Fourier heat conduction; non-Fickean diffusion; fractional calculus; Mittag-Leffler functions

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Zentralblatt MATH Berlin [Germany]