A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative
In this paper, we investigate the regularization of the backward problem for a diffusion process with a time-fractional derivative. We propose a novel double-parameter regularization scheme that integrates the quasi-reversibility method for the governing equation with the quasi-boundary method. Theo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/459 |
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| author | Qun Chen Zewen Wang |
| author_facet | Qun Chen Zewen Wang |
| author_sort | Qun Chen |
| collection | DOAJ |
| description | In this paper, we investigate the regularization of the backward problem for a diffusion process with a time-fractional derivative. We propose a novel double-parameter regularization scheme that integrates the quasi-reversibility method for the governing equation with the quasi-boundary method. Theoretical analysis establishes the regularity and the convergence analysis of the regularized solution, along with a convergence rate under an <i>a-priori</i> regularization parameter choice rule in the general-dimensional case. Finally, numerical experiments validate the effectiveness of the proposed scheme. |
| format | Article |
| id | doaj-art-ad11c4d6f22b43b0b5d2eee9978ae032 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-ad11c4d6f22b43b0b5d2eee9978ae0322025-08-20T03:07:58ZengMDPI AGFractal and Fractional2504-31102025-07-019745910.3390/fractalfract9070459A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional DerivativeQun Chen0Zewen Wang1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaSchool of Arts and Sciences, Guangzhou Maritime University, Guangzhou 510725, ChinaIn this paper, we investigate the regularization of the backward problem for a diffusion process with a time-fractional derivative. We propose a novel double-parameter regularization scheme that integrates the quasi-reversibility method for the governing equation with the quasi-boundary method. Theoretical analysis establishes the regularity and the convergence analysis of the regularized solution, along with a convergence rate under an <i>a-priori</i> regularization parameter choice rule in the general-dimensional case. Finally, numerical experiments validate the effectiveness of the proposed scheme.https://www.mdpi.com/2504-3110/9/7/459backward problemtime-fractional diffusion equationdouble-parameter regularizationconvergence rate |
| spellingShingle | Qun Chen Zewen Wang A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative Fractal and Fractional backward problem time-fractional diffusion equation double-parameter regularization convergence rate |
| title | A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative |
| title_full | A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative |
| title_fullStr | A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative |
| title_full_unstemmed | A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative |
| title_short | A Double-Parameter Regularization Scheme for the Backward Diffusion Problem with a Time-Fractional Derivative |
| title_sort | double parameter regularization scheme for the backward diffusion problem with a time fractional derivative |
| topic | backward problem time-fractional diffusion equation double-parameter regularization convergence rate |
| url | https://www.mdpi.com/2504-3110/9/7/459 |
| work_keys_str_mv | AT qunchen adoubleparameterregularizationschemeforthebackwarddiffusionproblemwithatimefractionalderivative AT zewenwang adoubleparameterregularizationschemeforthebackwarddiffusionproblemwithatimefractionalderivative AT qunchen doubleparameterregularizationschemeforthebackwarddiffusionproblemwithatimefractionalderivative AT zewenwang doubleparameterregularizationschemeforthebackwarddiffusionproblemwithatimefractionalderivative |