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The time fractional diffusion equation and the advection-dispersion equation. (English) Zbl 1072.35218
Authors’ abstract: “The authors obtain explicit relationships between the time fractional diffusion equation and the advection-dispersion equation in the whole-space with the corresponding problems in the half-space using the Fourier-Laplace transform. Furthermore, they investigate the time fractional advection-dispersion equation in a bounded space domain.”
##### MSC:
 35S30 Fourier integral operators 26A33 Fractional derivatives and integrals (real functions) 76R50 Diffusion (fluid mechanics) 35A22 Transform methods (PDE)