An inverse Sturm–Liouville problem with a fractional derivative Academic Article uri icon

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 . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.

author list (cited authors)

  • Jin, B., & Rundell, W.

citation count

  • 19

publication date

  • May 2012