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The fractional diffusion model with an absorption term and modified Fick’s law for non-local transport processes. (English) Zbl 1196.37120
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 ν on the probability density is greater than that of the fractional oscillator parameter β. The effect range of ν on a probability density is opposite to that of β. This paper provides a new analytical tool to develop fluid mechanics, heat conduction and other engineering sciences.
37L99Infinite-dimensional dissipative dynamical systems
60J65Brownian motion
76D05Navier-Stokes equations (fluid dynamics)
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