SPECTRAL ANALYSIS FOR DISCONTINUOUS CONFORMABLE STURM-LIOUVILLE PROBLEMS WITH SPECTRAL PARAMETER CONTAINED IN BOUNDARY CONDITIONS

Abstract

In this study, we consider a discontinuous Sturm-Liouville problem with eigenvalue dependent on the boundary condition in the sense of conformable derivative. We prove that the discontinuous conformable Sturm-Liouville operator is symmetric, the eigenvalues are real and the eigenfunctions corresponding to different eigenvalues are orthogonal. We obtain the representations of the solutions under different initial conditions for this kind of problem and give the asymptotics for the eigenfunctions and eigenvalues. Also, visual results are demonstrated for different orders and different potentials by graphs to check the behaviour of the solutions.