Ambarzumyan-type theorem with local derivative

We show the Ambarzumyan theorem in this paper by considering the Sturm-Liouville problem with separable boundary conditions and local derivatives. We prove that if the spectrum consists of the first eigenvalue, then the potential function can be found depending on the first eigenvalue. Also, we give some examples like periodic and anti-periodic boundary conditions. In the case of α = ۱, the results of the classical case can be obtained. Although the concept of conformable fractional is debatable, we think the results will be useful for Sturm-Liouville theory.

کلیدواژه ها:

Ambarzumyan theorem ، Sturm-Liouville problem ، conformable derivatives and integrals ، eigenvalues