Integro-differential diffusion equation for continuous time random walk
| Autor: | Fa, Kwok Sau, Wang, K. G. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | PRE 81, 011126 (2010) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.81.011126 |
| Popis: | In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution. Comment: 12 pages |
| Databáze: | arXiv |
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