Inverse problems for the time-fractional diffusion equation with multiplicative Brownian motion
Abstract
Abstract In this paper, we consider inverse problems for a time-fractional diffusion equation with multiplicative Brownian motion. First, the well-posedness of the direct problem is established. Then, the uniqueness and instability for reconstructing the spatial source from the expectation of terminal data are proved. Furthermore, building upon the uniqueness theory for the fractional order, the identifiability of the order using finite-time observations is established under specific conditions on the temporal source. Finally, a numerical algorithm is developed for the specific equation, and several numerical examples are provided to illustrate the theoretical results.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Numerical methods in inverse problems
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Physica Scripta
- Publisher
- IOP Publishing
- Volume
- 101
- Issue
- 29
- Pages
- 295205–295205
- Publication date
- 14 July 2026