University of Tabriz Computational Methods for Differential Equations 2345-3982 12 3 2024 05 01 An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem 471 483 17114 10.22034/cmde.2023.57436.2403 EN Hanif Mirzaei Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. Mahmood Emami Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. Kazem Ghanbari Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. Mohammad Shahriari Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran. Journal Article 2023 07 08 In this paper, Computing the eigenvalues of the Conformable Sturm-Liouville Problem (CSLP) of order $2 \alpha$, $\frac{1}{2}<\alpha \leq 1$, and dirichlet boundary conditions is considered. For this aim, CSLP is discretized to obtain a matrix eigenvalue problem (MEP) using finite element method with fractional shape functions. Then by a method based on the asymptotic form of the eigenvalues, we correct the eigenvalues of MEP to obtain efficient approximations for the eigenvalues of CSLP. Finally, some numerical examples to show the efficiency of the proposed method are given. Numerical results show that for the $n$th eigenvalue, the correction technique reduces the error order from $O(n^4h^2)$ to $O(n^2h^2)$. https://cmde.tabrizu.ac.ir/article_17114_243b85e9d190741b80f2ad25cd182df0.pdf