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

Y. Z. Povstenko

Mathematical Problems in Engineering, 2014, vol. 2014, 1-7

Abstract:

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:705364

DOI: 10.1155/2014/705364

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