University of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Inverse Conformable Sturm-Liouville Problems with a Transmission and Eigen-Parameter Dependent Boundary Conditions8710470752510.22130/scma.2023.2000439.1297ENMohammadShahriariDepartment of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136-553, Maragheh, Iran.0000-0002-8982-2451RezaAkbariDepartment of Mathematical Sciences, Payame Noor University, Iran.0000-0000-0000-0000Journal Article20230418In 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.https://scma.maragheh.ac.ir/article_707525_aafd716f583bfc4cdc6dbb878dbb855a.pdf