TWO REGULARIZATION METHODS FOR IDENTIFYING THE SOURCE TERM PROBLEM ON THE TIME-FRACTIONAL DIFFUSION EQUATION WITH A HYPER-BESSEL OPERATOR

doi:10.1007/s10473-022-0412-5

摘要/Abstract

摘要： In this paper, we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator. First, we prove that this inverse problem is ill-posed, and give the conditional stability. Then, we give the optimal error bound for this inverse problem. Next, we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem, and give corresponding error estimates under different regularization parameter selection rules. Finally, we verify the effectiveness of the method through numerical examples.

关键词: Time-fractional diffusion equation, source term problem, fractional Landweber regularization method, Hyper-Bessel operator, fractional Tikhonov regularization method

Abstract: In this paper, we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator. First, we prove that this inverse problem is ill-posed, and give the conditional stability. Then, we give the optimal error bound for this inverse problem. Next, we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem, and give corresponding error estimates under different regularization parameter selection rules. Finally, we verify the effectiveness of the method through numerical examples.

Key words: Time-fractional diffusion equation, source term problem, fractional Landweber regularization method, Hyper-Bessel operator, fractional Tikhonov regularization method

中图分类号:

35R25

杨帆, 孙乔夕, 李晓晓. TWO REGULARIZATION METHODS FOR IDENTIFYING THE SOURCE TERM PROBLEM ON THE TIME-FRACTIONAL DIFFUSION EQUATION WITH A HYPER-BESSEL OPERATOR[J]. 数学物理学报(英文版), 2022, 42(4): 1485-1518.

Fan YANG, Qiaoxi SUN, Xiaoxiao LI. TWO REGULARIZATION METHODS FOR IDENTIFYING THE SOURCE TERM PROBLEM ON THE TIME-FRACTIONAL DIFFUSION EQUATION WITH A HYPER-BESSEL OPERATOR[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1485-1518.

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