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.

In this paper, Computing the eigenvalues of the Conformable Sturm-Liouville Problem (CSLP) of order ۲ \alpha, \frac{۱}{۲}<\alpha \leq ۱, 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 nth eigenvalue, the correction technique reduces the error order from O(n^۴h^۲) to O(n^۲h^۲).

Sturm-Liouville problem, Conformable derivative, Finite elements method, Correction idea