Two regularization methods for identifying the source term of Caputo–Hadamard time‐fractional diffusion equation

Abstract

In this paper, the inverse problem for identifying the unknown source on time‐fractional diffusion equation with Caputo–Hadamard derivative is considered. This problem is ill‐posed, and two regularization methods are used to solve it. Firstly, we prove that the problem is ill‐posed and give the conditional stability and the optimal error bound. Secondly, the error estimates of the fractional Landweber iterative regularization method and the fractional Tikhonov regularization method under a priori and a posteriori parameter selection rules are given, respectively. Finally, numerical examples are given to illustrate the effectiveness of two regularization methods.