Conformable Discontinuous Sturm-Liouville Problem with Applied Results

Abstract

In this article. we present some substantial spectral data for discontinuous fractional Sturm-Liouville equation involving conformable fractional derivative. We prove that the discontinuous fractional Sturm-Liouville operator is symmetric, the eigenvalues are real and the eigenfunctions corresponding to different eigenvalues are orthogonal. The given spectral data like representations of the solutions under different initial conditions. the asymptotics for the eigenfunctions and eigenvalues are applied in terms of limit based local derivative. Also. visual results are demonstrated with graphics for different orders and different potentials to check the behaviours of the solutions.