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Two regularization methods for identifying the initial value of Caputo-Hadamard time-fractional diffusion equation.

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Title: Two regularization methods for identifying the initial value of Caputo-Hadamard time-fractional diffusion equation.
Authors: Li, Ruo-Hong1, Cao, Ying1, Yang, Fan1 yfggd114@163.com, Li, Xiao-Xiao1
Source: Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 3, p561-582. 22p.
Subjects: Mathematical regularization, Fractional calculus, Stability theory, Numerical analysis, Approximation error, Inverse problems, Partial differential equations
Abstract: In this paper, the inverse problem of identifying the unknown initial value for time fractional diffusion equation with Caputo-Hadamard derivative is considered. This problem is illposed and two regularization methods are used to solve it. Firstly, we prove that this problem is ill-posed. Secondly, the conditional stability result and the optimal error bound are given. Then, the error estimates of the Quasi-boundary regularization method and the fractional Landweber iterative regularization method under a priori and a posteriori regularization parameter selection rules are given respectively. Finally, numerical examples are given to illustrate the effectiveness of two regularization methods. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+%26+Analysis%22">Mathematical Modelling & Analysis</searchLink>. 2026, Vol. 31 Issue 3, p561-582. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink>
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  Data: In this paper, the inverse problem of identifying the unknown initial value for time fractional diffusion equation with Caputo-Hadamard derivative is considered. This problem is illposed and two regularization methods are used to solve it. Firstly, we prove that this problem is ill-posed. Secondly, the conditional stability result and the optimal error bound are given. Then, the error estimates of the Quasi-boundary regularization method and the fractional Landweber iterative regularization method under a priori and a posteriori regularization parameter selection rules are given respectively. Finally, numerical examples are given to illustrate the effectiveness of two regularization methods. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3846/mma.2026.23999
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      – Code: eng
        Text: English
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        PageCount: 22
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      – SubjectFull: Mathematical regularization
        Type: general
      – SubjectFull: Fractional calculus
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      – SubjectFull: Stability theory
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      – SubjectFull: Numerical analysis
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      – SubjectFull: Approximation error
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      – SubjectFull: Inverse problems
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      – SubjectFull: Partial differential equations
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            – D: 01
              M: 07
              Text: 2026
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              Y: 2026
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