publication . Preprint . 2018

Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro;
Open Access English
  • Published: 17 Feb 2018
Abstract
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion Laplace transforms, it turns out that the decay rate of the solution for long time is dominated by the lowest order of the time-fractional derivatives. Finally, as an applica...
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free text keywords: Mathematics - Analysis of PDEs
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