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

Long Shi, Zuguo Yu, Zhi Mao, Aiguo Xiao and Hailan Huang

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 23, 5801-5807

Abstract: 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.

Keywords: Space–time fractional diffusion equation; Caputo fractional derivative; Riesz fractional derivative; Coupled continuous time random walk; Asymptotic behavior (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:23:p:5801-5807

DOI: 10.1016/j.physa.2013.08.021

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