A Note on Lyapunov-Type Inequalities for Fractional Boundary Value Problems with Sturm-Liouville Boundary Conditions

In this note, we study Cauchy-Schwarz-type inequality for fractional Strum-Liouville boundary value problem containing Caputo derivative of order a, 1 < a<- 2. A lower bound for the smallest eigenvalue is determined using this inequality. We give a comparison between the smallest eigenvalue and its lower bound obtained from the Lyapunov-type and Cauchy-Schwarz-type inequalities which indi- cate the properties of eigenvalues.