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

• Hikmet Koyunbakan ^[1] ; Kamal Shah ^[2] ; Thabet Abdeljawad ^[3]
  1. [1] Fırat University

     Fırat University

     Turquía

     
  2. [2] Prince Sultan University & University of Malakand
  3. [3] Prince Sultan University & China Medical University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • 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 wellposedness of the problem in the rest of study. We have basically shown that the set of potential functions satisfying the condition π 0 q(t)dαt < ∞ 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 α = 1, the results coincide with the results given for classical derivative problem