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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/7/459 |
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| Summary: | 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. |
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| ISSN: | 2504-3110 |