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

作者：Ruo-Hong Li, Ying Cao, Fan Yang, Xiaoxiao Li · 发表于：Mathematical Modelling and Analysis · 年份：2026 · DOI：10.3846/mma.2026.23999 · 研究领域：Fractional Differential Equations Solutions、Numerical methods in inverse problems、Advanced Control Systems Design

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.