Eigenvalue Corrections for a Perturbed Conformable Sturm-Liouville Problem

We apply the Rayleigh-Schrödinger perturbation scheme to aconformable Sturm-Liouville problem with Dirichlet boundary conditions on aweighted Hilbert space. The unperturbed problem has explicit trigonometriceigenfunctions, which allow a closed form analysis of localizedperturbations. For a point interaction, we derive the first and second ordereigenvalue corrections and analyze their dependence on the interactionlocation and the conformable parameter. We examine the critical point andendpoint behavior and obtain distinct endpoint thresholds of the conformableparameter. Finally, integrating the first order point response over reflectedintervals gives a closed formula for the left-right asymmetry of a stepperturbation and its large mode limit.