The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes

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 Mittag-Leffler function using finite Hankel integral transformation and Laplace transformation. In addition, numerical simulations are discussed. The results show that the effect range of time-fractional derivative V on probability density is greater than that of fractional oscillator parameter P. The effect range of v on probability density is opposite to that of P. This paper provides a new analytical tool to develop fluid mechanics, heat conduction and other engineering science. (C) 2008 Elsevier Ltd. All rights reserved.