Discontinuous fractional Sturm–Liouville problems with transmission conditions

摘要

The main purpose of this study is the investigation of discontinuous Sturm–Liouville problem with fractional derivatives. We give an operator theoretic framework of the problem under consideration. Namely, we define an operator A in the Hilbert space the eigenvalues and corresponding eigenfunctions of which coincide with the eigenvalues and corresponding eigenfunctions of the boundary value problem, respectively. Then, we establish the characteristic function and prove that the eigenvalues of the considered problem coincide with the roots of this characteristic function.