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

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	Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator
	Yang, Fan; Sun, Qiaoxi; Li, Xiaoxiao
刊名	ACTA MATHEMATICA SCIENTIA
	2022-04-01
卷号	42 期号:4 页码:1485-1518
关键词	Time-fractional diffusion equation source term problem fractional Landweber regularization method Hyper-Bessel operator fractional Tikhonov regularization method
ISSN号	0252-9602
DOI	10.1007/s10473-022-0412-5
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000814234200012
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/158831]
专题	理学院
作者单位	Lanzhou Univ Technol, Dept Math, Lanzhou 730000, Peoples R China
推荐引用方式 GB/T 7714	Yang, Fan,Sun, Qiaoxi,Li, Xiaoxiao. Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator[J]. ACTA MATHEMATICA SCIENTIA,2022,42(4):1485-1518.
APA	Yang, Fan,Sun, Qiaoxi,&Li, Xiaoxiao.(2022).Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator.ACTA MATHEMATICA SCIENTIA,42(4),1485-1518.
MLA	Yang, Fan,et al."Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator".ACTA MATHEMATICA SCIENTIA 42.4(2022):1485-1518.