TY - JOUR
T1 - A Generalized Quasi-Boundary Value Method for an Inverse Source Problem in a Distributed Order Time-Fractional Diffusion Equation
AU - Wu , Wenjie
AU - Wei , Ting
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 835
EP - 866
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-058.310824
UR - https://global-sci.org/intro/article_detail/eajam/24199.html
KW - Inverse source problem, distributed order time-fractional diffusion equation, generalized quasi-boundary value method, convergence rate, numerical experiment.
AB - <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>