Spectral Expansion for Conformable Fractional Sturm- Liouville Problem on the Whole Line

Abstract

In this article, we discuss a conformable fractional Sturm-Liouville boundary-value problem on the whole line. We prove the existence of a spectral function for the singular conformable fractional Sturm-Lioville problem. Further, we establish a Parseval equality and spectral expansion formula by terms of the spectral function for conformable fractional Sturm-Liouville problem on the whole line.