Uniqueness of the potential in conformable Sturm-Liouville problem - Koyunbakan, Hikmet (Wiley, 2023)
This study is about the inverse problem of the conformable Sturm-Liouville problem SLP. Namely, we first defined the problem with separable boundary conditions and gave some of its spectral properties. Then, by spectral data, we showed that the potential and the constants (c1,c2) in the boundary conditions are coincident for two different problems. Here, the potential is in the space L-alpha(2). We have also shown that if the potential function has the property of being symmetrical, only one spectrum is sufficient to find this function as uniquely. It is worth remembering that the methods and calculations used here are similar to those in the SLP with classical derivative. However, we think results will be valuable in Sturm-Liouville theory.
Keywords: fractional calculus; spectrum; Sturm-Liouville equation