Core Principles of Spectral Analysis in Fractional Singular Sturm–Liouville Systems

Fractional Singular Sturm–Liouville Systems

Abstract

This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper we investigate a spectral theory for the eigenvalues and 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.