Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

作者：Shi, Long; Yu, Zuguo^*; Mao, Zhi; Xiao, Aiguo; Huang, Hailan

来源：Physica A: Statistical Mechanics and Its Applications , 2013, 392(23): 5801-5807.

DOI：10.1016/j.physa.2013.08.021

• Space-time fractional diffusion equation
• Caputo fractional derivative
• Riesz fractional derivative
• Coupled continuous time random walk
• Asymptotic behavior

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.

• 出版日期2013-12-1
• 单位湘潭大学