Nguyen Hoang Tuana, Le Xuan Daib
aVietnam National University, Ho Chi Minh City, Vietnam (VNU–HCM).
bDepartment of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet, District 10, Ward 14, Ho Chi Minh City, Vietnam.
The paper discusses the inverse problem of determining an unknown source term in a fractional elliptic equation in a bounded domain. In order to solve the considered problem, a fractional Tikhonov method is used. Applying this method, a regularized solution is constructed. An a priori and a posteriori error estimate are obtained, and the case when the terminal data has random noise is also considered.
Keywords: Regularization method; Fractional pseudo-parabolic problem; Ill-posed problem; Nonlocal problem; Convergence estimates.
Nguyen, H. T., & Le, X. D. (2023). Reconstruct the unknown source for the fractional elliptic equations: Regularization method and error estimates. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 206–217.