Determination of three parameters in a time-space fractional diffusion equation

In this paper, we consider a nonlinear inverse problem of recovering two fractional orders and a diffusion coefficient in a one-dimensional time-space fractional diffusion equation. The uniqueness of fractional orders and the diffusion coefficient, characterizing slow diffusion, can be obtained from...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 6; pp. 5909 - 5923
Main Authors Xiong, Xiangtuan, Shi, Wanxia, Xue, Xuemin
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
fractional diffusion equation
ill-posedness
regularization
uniqueness
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Summary:In this paper, we consider a nonlinear inverse problem of recovering two fractional orders and a diffusion coefficient in a one-dimensional time-space fractional diffusion equation. The uniqueness of fractional orders and the diffusion coefficient, characterizing slow diffusion, can be obtained from the accessible boundary data. Two computational methods, Tikhonov method and Levenberg-Marquardt method, are proposed to solving this problem. Finally, an example is presented to illustrate the efficiency of the two numerical algorithm.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021350