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Mathematical Problems in Engineering
Volume 2014, Article ID 705364, 7 pages
Research Article

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

Institute of Mathematics and Computer Science, Jan Długosz University in Częstochowa, Waszyngtona 4/8, 42-200 Częstochowa, Poland

Received 28 December 2013; Accepted 6 February 2014; Published 11 March 2014

Academic Editor: J. A. Tenreiro Machado

Copyright © 2014 Y. Z. Povstenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.