Mohammad Shahriari - Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box ۵۵۱۳۶-۵۵۳, Maragheh, Iran.
Reza Abari - Department of Mathematical Sciences, Payame Noor University, Iran.

In this paper, we provide a different  uniqueness results for inverse spectral problems of conformable fractional Sturm-Liouville operators of order \alpha (۰ < \alpha\leq  ۱), 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.

Inverse Sturm-Liouville problem, Conformable fractional derivative, Internal discontinuities, Parameter-dependent boundary conditions