The Fractional Landweber method for identifying unknown source for the fractional elliptic equations

Doan Vuong Nguyen; Tuan NguyenHoang; Vo Viet  Tri

doi:10.61383/ejam.20242489

Authors

Doan Vuong Nguyen Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-9438-6439
Nguyen Hoang Tuan University of Health Sciences, Dong Hoa Ward, Di An City, Binh Duong Province, Vietnam https://orcid.org/0000-0003-4354-2937
Vo Viet Tri Division of Applied Mathematics, Thu Dau Mot University, 06 Tran Van On, Thu Dau Mot City, Binh Duong Province, Vietnam Corresponding Author https://orcid.org/0000-0002-8481-7469

DOI:

https://doi.org/10.61383/ejam.20242489

Keywords:

Convergence estimates, Regularization method, Ill-posed problem, Nonlocal problem

Abstract

The article addresses the inverse problem of identifying an unknown source term in a fractional elliptic equation defined in a bounded domain. The approach to solving the problem under consideration, the Landweber fractional method is used. This method involves constructing a regularization algorithm. A posteriori and a priori lapses estimates are obtained, and final data with random data is regard.

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