Spectral Properties and Approximation Results for Fractional Singular Sturm–Liouville Problems

Abstract

eigenfunctions of fractional singular Sturm–Liouville problem of Bessel

type by constructing a complete spectral decomposition. We show that all

eigenvalues are real and the corresponding eigenfunctions are orthogonal.

Risk upper bounds are obtained and new approximation results concerning

the spectral properties of the problem are established and rigorously

justified.