Identifying the source terms and initial values for fractional diffusion equation with stochastic terms interference
Abstract
Abstract In this paper, we consider the forward and inverse problem of the stochastic time-space differential equation with Caputo-Fabrizio derivatives. First, we prove that the forward problem is well-posed, then give the stable estimation for the forward problem. Next, we study the inverse problem for identifying the source term and initial value. The inverse problem is ill - posed. We use the Tikhonov regularization method to solve this inverse problem. Under choosing regularization parameters in two ways ( a priori and a posteriori ), we derive error estimates between the regularization solution and the exact solution. Finally, we use numerical examples to show our method works well.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Stochastic processes and financial applications
Numerical methods in inverse problems
Publication details
- Journal / source
- Physica Scripta
- Publisher
- IOP Publishing
- Volume
- 101
- Issue
- 7
- Pages
- 075204–075204
- Publication date
- 29 January 2026