AMBARZUMYAN TYPE THEOREM WITH CONFORMABLE DERIVATIVE

Document Type : Research Paper

Authors

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

Abstract

In this paper, we show the Ambarzumyan theorem by taking
into account the Sturm-Liouville problem with separable boundary conditions
by local derivative. We prove that if the spectrum consists of the first
eigenvalue, then the potential function can be found depending on the first
eigenvalue. Also, we give some examples like periodic and anti-periodic
boundary conditions. In the case of α = 1, results were given in [32].
Although the concept of conformable fractional is debatable, we hope the
results will be useful for Sturm-Liouville theory.

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Main Subjects



Articles in Press, Accepted Manuscript
Available Online from 27 May 2025
  • Receive Date: 11 December 2024
  • Revise Date: 12 April 2025
  • Accept Date: 22 May 2025