An inverse nodal problem of a conformable Sturm-Liouville problem with restrained constant delay

Abstract

This paper presents a new technique: a conformable derivative for the inverse problem of a Sturm-Liouville problem with restrained constant delay. Solutions to the Sturm-Liouville problem often involve eigenfunctions and eigenvalues, which have important applications in physics, engineering, and other fields. The presence of a constant delay introduces unique challenges in formulating and solving this problem. In this case, we derived the asymptotic formulas for the eigenvalues with their corresponding eigenfunctions and demonstrated the existence of the solution. Additionally, we identified the nodal points used to generate the problem's potential function. Finally, we applied the Lipschitz stability approach and demonstrated the stability of the solution to the problem.