Time-fractional telegraph equations and telegraph processes with Brownian time

• 成果类型: Article
• 署名作者: Orsingher, E; Beghin, L
• 署名单位: Sapienza University Rome
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0309-8
• 发表日期: 2004
• 页码: 141-160
• 关键词: heat-equation; integrodifferential equation; wave-equations; diffusion; LAWS

摘要

We study the fundamental solutions to time-fractional telegraph equations of order 2alpha. We are able to obtain the Fourier transform of the solutions for any alpha and to give a representation of their inverse, in terms of stable densities. For the special case alpha=1/2, we can show that the fundamental solution is the distribution of a telegraph process with Brownian time. In a special case, this becomes the density of the iterated Brownian motion, which is therefore the fundamental solution to a fractional diffusion equation of order 1/2 with respect to time.