An inverse Sturm-Liouville problem with a fractional derivative

Abstract

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order $\alpha \in (1,2)$ of fractional derivative is sufficiently away from 2.

16 pages, 6 figures, accepted for publication in Journal of Computational Physics

References in corpus (1)

• A Least Squares Functional for Solving Inverse Sturm-Liouville Problems

Cited by in corpus (4)

• Recovering an Unknown Source in a Fractional Diffusion Problem
• A Finite Element Method for the Fractional Sturm-Liouville Problem
• Variational formulation of problems involving fractional order differential operators
• Theorem of Existence and Uniqueness of Solution for Differential Equation of Fractional Order