A stability result for the determination of order in time-fractional diffusion equations

  • 1 School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong, P. R. China
  • 2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan
  • 3 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan
Zhiyuan LiORCID iD: https://orcid.org/0000-0002-5961-7211, Xinchi Huang
  • Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
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and Masahiro YamamotoORCID iD: https://orcid.org/0000-0002-4050-871X
  • Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan, and Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, no 54, 050094 Bucharest Romania; and Peoples’ Friendship University of Russia (RUDN University) 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • orcid.org/0000-0002-4050-871X
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar


This paper deals with an inverse problem of the determination of the fractional order in time-fractional diffusion equations from one interior point observation. We give a representation of the solution via the Mittag-Leffler function and eigenfunction expansion, from which the Lipschitz stability of the fractional order with respect to the measured data at the interior point is established.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.