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Fractional nonlinear diffusion equation and first passage time

Author

Listed:
  • Wang, Jun
  • Zhang, Wen-Jun
  • Liang, Jin-Rong
  • Xiao, Jian-Bin
  • Ren, Fu-Yao

Abstract

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with a space- and time-dependent diffusion coefficient subject to absorbing boundaries and the initial condition. We obtain explicit analytical expression for the probability distribution, the first passage time distribution, the mean first passage time, and the mean squared displacement corresponding to different time-dependent diffusion coefficient. In addition, we compare our results for the first passage time distribution and the mean first passage time with the one obtained by usual linear diffusion equation with time-dependent diffusion coefficient.

Suggested Citation

  • Wang, Jun & Zhang, Wen-Jun & Liang, Jin-Rong & Xiao, Jian-Bin & Ren, Fu-Yao, 2008. "Fractional nonlinear diffusion equation and first passage time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 764-772.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:4:p:764-772
    DOI: 10.1016/j.physa.2007.10.021
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    Citations

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    Cited by:

    1. Di Zhang & Roderick V. N. Melnik, 2009. "First passage time for multivariate jump‐diffusion processes in finance and other areas of applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 565-582, September.
    2. Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015. "First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 279-290.
    3. Wang, Jun & Zhang, Wen-Jun & Liang, Jin-Rong & Zhang, Pan & Ren, Fu-Yao, 2008. "Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4547-4552.

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