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Spectral data of conformable Sturm–Liouville direct problems

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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 Sturm–Liouville (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 \(\alpha \)-orthogonality of eigenfunctions for CSLPs defined by Abdeljawad and Al-Refai (Complexity vol 2017, Article ID 3720471, 2017) in the last section.

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Authors and Affiliations

  1. Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey

    Erdal Bas, Ramazan Ozarslan & Ahu Ercan

  2. Department of Mathematics, Science Faculty, Bartin University, Bartin, Turkey

    Funda Metin Turk

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  1. Erdal Bas
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  2. Funda Metin Turk
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  3. Ramazan Ozarslan
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  4. Ahu Ercan
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Correspondence to Erdal Bas.

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Bas, E., Metin Turk, F., Ozarslan, R. et al. Spectral data of conformable Sturm–Liouville direct problems. Anal.Math.Phys. 11, 8 (2021). https://doi.org/10.1007/s13324-020-00428-6

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  • DOI: https://doi.org/10.1007/s13324-020-00428-6

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