Inverse Conformable Sturm-Liouville Problems with a Transmission and Eigen-Parameter Dependent Boundary Conditions

Abstract

In this paper, we provide a different uniqueness results for inverse spectral problems of conformable fractional Sturm-Liouville operators of order $\alpha$ ($0 < \alpha\leq 1$), with a jump and eigen-parameter dependent boundary conditions. Further, we study the asymptotic form of solutions, eigenvalues and the corresponding eigenfunctions of the problem. Also, we consider three terms of the inverse problem, from the Weyl function, the spectral data and two spectra. Moreover, we can also extend Hald's theorem to the problem.

Keywords

• inverse sturm-liouville problem
• conformable fractional derivative
• internal discontinuities
• parameter-dependent boundary conditions