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

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 meth...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-07, Vol.15 (7), p.1468
Main Authors: Chen, Yong-Gang, Yang, Fan, Tian, Feng
Format: Article
Language:English
Subjects:
Caputo–Fabrizio fractional derivative
Hilbert space
identifying the unknown source
Ill posed problems
Inequality
inverse problem
Inverse problems
Iterative methods
Landweber iterative regularization method
Mathematical functions
Parameters
Regularization
Regularization methods
time-fractional diffusion equation
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15071468