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First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval

Author

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  • Guo, Gang
  • Chen, Bin
  • Zhao, Xinjun
  • Zhao, Fang
  • Wang, Quanmin

Abstract

We investigate the first passage time (FPT) distribution for accelerating subdiffusion governed by the modified fractional diffusion equation which has a secondary fractional time derivative acting on a diffusion operator. For the FPT problem subject to absorbing barrier condition, we obtain exact analytical expressions for the FPT distribution as well as its Laplace transform in the semi-infinite interval. Most of the results have been derived by using the Laplace transform, the Fourier Cosine transform, the Mellin transform and the properties of the Fox H-function. In contrast to the Laplace transform of the FPT distribution which can be expressed elegantly and neatly, the exact solution for the FPT distribution requires an infinite series of Fox H-functions instead of a single Fox H-function. Numerical result reveals that the crossover between the two distinct scaling regimes is apparent only when the discrepancy between the two diffusion exponents becomes more pronounced.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:433:y:2015:i:c:p:279-290
    DOI: 10.1016/j.physa.2015.04.005
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    References listed on IDEAS

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