@Article{EAJAM-15-835,
author = {Wu , Wenjie and Wei , Ting},
title = {A Generalized Quasi-Boundary Value Method for an Inverse Source Problem in a Distributed Order Time-Fractional Diffusion Equation},
journal = {East Asian Journal on Applied Mathematics},
year = {2025},
volume = {15},
number = {4},
pages = {835--866},
abstract = {<p style="text-align: justify;">Subdiffusion equations with distributed-order fractional derivatives describe
important physical phenomena. In this paper, we consider an inverse space-dependent
source term problem governed by a distributed order time-fractional diffusion equation using final time data. Based on the series expression of the solution, the inverse
source problem can be transformed into a first kind of Fredholm integral equation. The
existence, uniqueness and a conditional stability of the considered inverse problem are
established. Building upon this foundation, a generalized quasi-boundary value regularization method is proposed to solve the inverse source problem, and then we prove the
well-posedness of the regularized problem. Further, we provide the convergence rates
of the regularized solution by employing an a priori and an a posteriori regularization
parameter choice rule. Numerical examples in one-dimensional and two-dimensional
cases are provided to validate the effectiveness of the proposed method.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2024-058.310824},
url = {http://global-sci.org/intro/article_detail/eajam/24199.html}
}