The Landweber Iterative Regularization Method for Identifying the Unknown Source of Caputo-Fabrizio Time Fractional Diffusion Equation on Spherically Symmetric Domain

Abstract

In this article, the inverse problem for identifying the space-dependent source of time fractional diffusion equation on a spherically symmetric domain with Caputo–Fabrizio fractional derivative is discussed. This problem is a typical ill-posed problem and the Landweber iterative regularization method is used to obtain the approximation solution. The convergent error estimates under a priori regularization parameter choice rule and a posteriori regularization parameter choice rule are given, respectively. The numerical examples are given to show the effectiveness of the Landweber iterative regularization method.

Keywords

• inverse problem
• time-fractional diffusion equation
• Caputo–Fabrizio fractional derivative
• identifying the unknown source
• Landweber iterative regularization method