An inverse Sturm-Liouville problem with a fractional derivative

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 is an element of (1,2) of fractional derivative is sufficiently away from 2. (C) 2012 Elsevier Inc. All rights reserved.