Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

作者：Li Zhiyuan^*; Luchko Yuri; Yamamoto Masahiro

来源：Fractional Calculus and Applied Analysis, 2014, 17(4): 1114-1136.

DOI：10.2478/s13540-014-0217-x

• distributed order fractional diffusion equation
• initial-boundary-value problems
• short-time asymptotic behavior
• long-time asymptotic behavior
• Laplace transform

This article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t -> 0 and t -> +a. By the Laplace transform method, we show that the solutions decay logarithmically as t -> +a. As t -> 0, the decay rate of the solutions is dominated by the term (t log(1/t))(-1). Thus the asymptotic behavior of solutions to the initial-boundary-value problem for the distributed order time-fractional diffusion equations is shown to be different compared to the case of the multi-term fractional diffusion equations.

• 出版日期2014-12