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

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

Physica A: Statistical Mechanics and its Applications, 2015, vol. 433, issue C, 279-290

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.

Keywords: First passage time; Accelerating subdiffusion; Modified fractional diffusion equation; Semi-infinite interval; Fox H-function (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:433:y:2015:i:c:p:279-290

DOI: 10.1016/j.physa.2015.04.005

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