Computational of the eigenvalues of the fractional Sturm-Liouville problem

We study the asymptotic distribution for eigenvalues of fourth-order fractional Sturm-Liouville with Dirichlet boundary condition. In this work, we use the inverse Laplace transform method and the Asymptotic formula of the Mittag-Leffler function to get an analytical solution of the fractional Sturm-Liouville problems. When the fractional-order approaches 1, our results agree with the classical ones of fourth-order differential equations.