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

• Published in: Physica A Vol. 433; pp. 279 - 290
• Main Authors: Guo, Gang, Chen, Bin, Zhao, Xinjun, Zhao, Fang, Wang, Quanmin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2015
• Subjects: Accelerating subdiffusion; First passage time; Fox [formula omitted]-function; Modified fractional diffusion equation; Semi-infinite interval; Semi-infinite interval; First passage time; Fox H-function; Accelerating subdiffusion; Modified fractional diffusion equation
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2015.04.005

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. •We find the first passage time of a modified fractional equation for accelerating subdiffusion.•The crossover of the first passage time between two distinct scaling regimes is revealed.•The scaling behavior is different from that of the aging diffusion.