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Well-Posedness of Inverse Sturm–Liouville Problem with Fractional Derivative

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Abstract

We have given the inverse nodal problem for the fractional Sturm–Liouville (S–L) problem and the stability for this problem. First of all, we have shown asymptotic forms for nodal parameters and by them, the potential function can be reconstructed with a limit of nodal parameters. We proved that this limit exists. We also gave well-posedness of the problem in the rest of study. We have basically shown that the set of potential functions satisfying the condition \(\int _{0}^{\pi }q(t)d_{\alpha }t<\infty \) is homeomorphic to the space of quasi nodal sequences. Although the results given in the paper were given for the classical derivative of S–L the problem, the results here are different and more general than the previous results because they contain the fractional derivative. If \(\alpha =1\), the results coincide with the results given for classical derivative problem.

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Acknowledgements

The authors Kamal Shah and Thabet Abdeljawad would like to thank Prince Sultan University for support through TAS research lab.

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Authors and Affiliations

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

    Hikmet Koyunbakan

  2. Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia

    Kamal Shah & Thabet Abdeljawad

  3. Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, 18000, Pakistan

    Kamal Shah

  4. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Thabet Abdeljawad

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  1. Hikmet Koyunbakan
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Koyunbakan, H., Shah, K. & Abdeljawad, T. Well-Posedness of Inverse Sturm–Liouville Problem with Fractional Derivative. Qual. Theory Dyn. Syst. 22, 23 (2023). https://doi.org/10.1007/s12346-022-00727-2

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  • DOI: https://doi.org/10.1007/s12346-022-00727-2

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