  In this paper, spectral analysis of fractional Sturm Liouville problem
defined on (0,1], having the singularity of type at zero and research 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. Furthermore,we give some important theorems and
lemmas for fractional hydrogen atom equation.
