Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
