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 α∈(1,2) of fractional derivative is sufficiently away from 2.Comment: 16 pages, 6 figures, accepted for publication in Journal of
Computational Physic