Working Paper Article Version 1 This version is not peer-reviewed

Spectral Data of Conformable Sturm-Liouville Direct Problems

Version 1 : Received: 24 December 2019 / Approved: 25 December 2019 / Online: 25 December 2019 (03:13:13 CET)

How to cite: Bas, E.; Metin Turk, F.; Ozarslan, R.; Ercan, A. Spectral Data of Conformable Sturm-Liouville Direct Problems. Preprints 2019, 2019120328 Bas, E.; Metin Turk, F.; Ozarslan, R.; Ercan, A. Spectral Data of Conformable Sturm-Liouville Direct Problems. Preprints 2019, 2019120328

Abstract

In this study, we investigate spectral structure of conformable Sturm-Liouville problems and with this end, we obtain representation of solutions under different initial conditions and asymptotic formulas for eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Also, we compare the solutions with graphics with different orders, different eigenvalues, different potentials and so, we observe the behaviors of eigenfunctions. We give an application to the α -orthogonality of eigenfunctions and reality of eigenvalues for conformable Sturm-Liouville problems defined by [15] in the last section.

Subject Areas

Sturm-Liouville; conformable derivative; asymptotic formula; spectral data

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