On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative

The asymptotics as $\alpha\to0+$ of the number of real eigenvalues $\lambda_n(\alpha)$ of the problem $y''(x)+\lambda D_{0}^{\alpha}y(x)=0$, $0<x<1$, $y(0)=y(1)=0$, is found. The minimization of real eigenvalues was carried out. It is proved that $\lim\limits_{\alpha\to0+}\lambda_n(\alpha)=(\pi n)^2$.