# Inverse problems for a conformable fractional Sturm-Liouville operator

## TL;DR

This paper investigates inverse problems for a conformable fractional Sturm-Liouville operator, establishing uniqueness theorems and exploring half-inverse problems with classical spectral data.

## Contribution

It introduces new uniqueness results and the Hochstadt-Lieberman-type theorem for inverse problems involving conformable fractional derivatives.

## Key findings

- Uniqueness theorems based on Weyl function and spectral data
- Results on half-inverse problems and spectral data reconstruction
- Extension of classical inverse spectral results to conformable fractional context

## Abstract

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study on half-inverse problem and prove a Hochstadt and Lieberman-type theorem.