Abstract. We obtain Lyapunov inequality and Hartman-Wintner-type inequality for two higherorder multi-point fractional boundary value problems. The technique of order-reduction and the properties of Green's function are important to our results. As applications, we discuss the eigenvalue problem and the real zeros for Mittag-Leffler function.Mathematics subject classification (2010): 26A33, 26D10, 33E12 , 34A08.