Regularization Method with Two Differential Operators for Simultaneous Inversion of Source Term and Initial Value in a Time-Fractional Black-Scholes Equation
Abstract
This paper is devoted to identifying the source term and initial value simultaneously in a time-fractional Black-Scholes equation, which is an ill-posed problem. The inverse problem is transformed into a system of operator equations, and under certain source conditions, conditional stability is established. We propose a regularization method with two differential operators to solve the problem, error estimates by rules of a priori and a posteriori regularization parameter selection are derived, respectively. Numerical experiments are presented to validate the effectiveness of the proposed regularization method.
Fields of Study & Subjects
Numerical methods in inverse problems
Fractional Differential Equations Solutions
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Computational Mathematics
- Volume
- 44
- Issue
- 5
- Pages
- 1526–1553
- Publication date
- 28 January 2026