Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables | Zendy

Yuriy Povstenko | Zendy

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Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables

Author(s) -

Yuriy Povstenko

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/705364

Subject(s) - mathematics , algorithm , diffusion , bessel function , mathematical analysis , physics , thermodynamics

The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to time and the Fourier transforms with respect to the space coordinates and . The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.

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