In this paper, we define a fractional singular Sturm-Liouville operator having Coulomb potential of type A x . Our main issue is to investigate the spectral properties for the operator. Furthermore, we prove new results according to the fractional singular Sturm-Liouville problem. MSC: 26A33; 34A08

In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0, 1], having the singularity of type () 2 1 2 l l r r + − + at zero and researched the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively.

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