Eigenvalue problems for fractional differential equations with right and left fractional derivatives

This paper studies the eigenvalue problem of a class of fractional differential equations with right and left fractional derivatives. With the aid of the spectral theory of compact self-adjoint operators in Hilbert spaces, we show that the spectrum of this problem consists of only countable real eigenvalues with finite multiplicity and the corresponding eigenfunctions form a complete orthogonal system. Furthermore, the lower bound of the eigenvalues is obtained.