Time fractional advection-dispersion equation
type: Item
instance of: scholarly article
title: Time fractional advection-dispersion equation
zbMATH Open document ID: 1068.26006
DOI: 10.1007/BF02936089
author: Fawang Liu
author: Vo V. Anh
author: I. Turner
author: P. Zhuang
published in: Journal of Applied Mathematics and Computing
publication date: 2004-05-18T00:00:00Z
review text: Applying first a simplifying substitution of the dependent variable (which in the end must be inverted) and then using the transforms of Laplace and Mellin the authors construct in terms of H-functions a representation of the fundamental solution to the linear time-fractional diffusion-convection equation (called by them ``advection dispersion-equation'') with constant coefficients. In this way they generalize the solution known for the special case of pure diffusion (dispersion) without convection (advection). By ``time-fractional'' they mean, as has become common language, replacement of the first time derivative by a fractional time derivative of order \(\alpha \in (0, 1]\). Actually, they use the fractional derivative suitably regularized at zero, usually now called the ``Caputo fractional derivative'' which is appropriate in handling Cauchy problems.
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 2064707
zbMATH Keywords: time-fractional advection-dispersion
zbMATH Keywords: Mellin transform
zbMATH Keywords: Laplace transform
zbMATH Keywords: H-functions
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02936089
OpenAlex ID: W2008474712
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description: scientific article; zbMATH DE number 2064707