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 \(\nu\) 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.
Reviewer: Fuhua Ling (Milpitas)
MSC:
| 37L99 | Infinite-dimensional dissipative dynamical systems |
| 60J65 | Brownian motion |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
fractional Fick’s law; Riemann-Liouville fractional derivative; anomalous diffusion; fractional oscillator; finite Handel transformationReferences:
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