An efficient method for solving regular variable fractional Sturm-Liouville problems

This article is devoted to both theoretical and numerical study of the eigenvalues of regular fractional Sturm-Liouville problem. The fractional derivative in this paper is in the conformable derivative sense. In this paper, we implement the reproducing kernel Hilbert space method to approximate the eigenvalues. Existence and uniformly convergent of the eigenfunctions of the considered problem are provided and proved. The main properties of the Sturm-Liouville problem are investigated. Numerical results demonstrate the accuracy of the present algorithm. Comparisons with other methods are presented.