In this paper, we consider a half-inverse Sturm–Liouville problem on a time scale which is the union of an interval and another time scale such as . We give a Hochstadt–Lieberman-type theorem for a Sturm–Liouville dynamic equation with Robin boundary conditions and investigate some special cases of this theorem.

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AbstractIn this paper, a Sturm–Liouville boundary value problem which includes conformable fractional derivatives of order α, {0<\alpha\leq 1} is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study the half-inverse problem and prove a Hochstadt–Lieberman-type theorem.

Özet: Bu makalede, difüzyon operatörlerinin pozitif özdeğerleri ile asal sayılar arasındaki ilişki incelenmiştir. Ayrıca, özdeğerleri, asal sayıların dağılımını gösteren Coulomb singularitesine sahip bir Sturm-Liouville problemi önerilmiştir.Anahtar kelimeler: Ters problem, spektrum, asal sayılar, difüzyon operator, coulomb singularite Eigenvalues of diffusion operators and Prime numbersAbstract. In this paper, the relationship between the positive eigenvalues of diffusion operators and prime numbers is investigated. We also propose a Sturm-Liouville problem with Coulomb singularity that shows eigenvalues the distribution of prime numbers.

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