The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes
type: Item
instance of: scholarly article
title: The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes
zbMATH Open document ID: 1196.37120
author: Mingyu Xu
author: Xiaoyun Jiang
author: Haitao Qi
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-01-12T00:00:00Z
review text: A generalized non-local Fick's law on fractal-dimension is derived. Using modified Fick's law a time-space fractional diffusion model with a fractional oscillator term is built. The solution is obtained in terms of a Mittag-Leffler function using a finite Hankel integral transformation and Laplace transformation. In addition, numerical simulations are discussed. The results show that the effect range of the time-fractional derivative \(\nu\) on the probability density is greater than that of the fractional oscillator parameter \(\beta\). The effect range of \(\nu\) on a probability density is opposite to that of \(\beta\). This paper provides a new analytical tool to develop fluid mechanics, heat conduction and other engineering sciences.
reviewed by: Fuhua Ling
Mathematics Subject Classification ID: 37L99
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 5656649
zbMATH Keywords: fractional Fick's law
zbMATH Keywords: Riemann-Liouville fractional derivative
zbMATH Keywords: anomalous diffusion
zbMATH Keywords: fractional oscillator
zbMATH Keywords: finite Handel transformation
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.10.057
OpenAlex ID: W2009155935
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DOI: 10.1016/J.NONRWA.2008.10.057
description: scientific article; zbMATH DE number 5656649