Spectral data of conformable Sturm-Liouville direct problems

Abstract

In this study, the spectral analysis of conformable Sturm-Liouville problems (CSLPs) are investigated in detail and to that end, the spectral analysis of classical SturmLiouville (SL) differential problems move to conformable analysis obtaining the representation of solutions and from this point of view asymptotic forms of spectral data, such as eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Moreover, we compare the solutions by means of illustrations with different arbitrary orders, different potential functions, different eigenvalues and so, we evaluate the behaviors of eigenfunctions. We give an important application to the reality of eigenvalues and a-orthogonality of eigenfunctions for CSLPs defined by Abdeljawad and Al-Refai (Complexity vol 2017, Article ID 3720471, 2017) in the last section.