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Volume 31, Issue 4
Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian

Jianlin Wang, Xiangtuan Xiong & Xiaoxiao Cao

DOI: 10.4208/jpde.v31.n4.4

J. Part. Diff. Eq., 31 (2018), pp. 333-342.

Published online: 2019-01

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  • Abstract

In this paper, we consider a time-fractional backward problem with a fractional Laplacian. We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule. Error estimates are proved. Some numerical examples are shown to verify the effectiveness of the proposed method.

  • Keywords

Inverse problem Ill-posedness error estimate fractional regularization method.

  • AMS Subject Headings

65R35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

1938854711@qq.com (Jianlin Wang)

xiongxt@gmail.com (Xiangtuan Xiong)

1160186216@qq.com (Xiaoxiao Cao)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-333, author = {Wang , JianlinXiong , Xiangtuan and Cao , Xiaoxiao}, title = {Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {31}, number = {4}, pages = {333--342}, abstract = {

In this paper, we consider a time-fractional backward problem with a fractional Laplacian. We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule. Error estimates are proved. Some numerical examples are shown to verify the effectiveness of the proposed method.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/12947.html} }
TY - JOUR T1 - Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian AU - Wang , Jianlin AU - Xiong , Xiangtuan AU - Cao , Xiaoxiao JO - Journal of Partial Differential Equations VL - 4 SP - 333 EP - 342 PY - 2019 DA - 2019/01 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/12947.html KW - Inverse problem KW - Ill-posedness KW - error estimate KW - fractional regularization method. AB -

In this paper, we consider a time-fractional backward problem with a fractional Laplacian. We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule. Error estimates are proved. Some numerical examples are shown to verify the effectiveness of the proposed method.

Wang , JianlinXiong , Xiangtuan and Cao , Xiaoxiao. (2019). Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian. Journal of Partial Differential Equations. 31 (4). 333-342. doi:10.4208/jpde.v31.n4.4
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