Hartman–Wintner and Lyapunov-type inequalities for high order fractional boundary value problems

Abstract

In this study, we derive   Hartman-Wintner and Lyapunov-type inequalities for the three-point fractional boundary value problem of the fractional Caputo differential equation of order $\alpha \in (2,3]$. These obtained inequalities are sharper than the existing results in the literature.   Some consequences of the results related to the fractional Sturm–Liouville eigenvalue problems have also been given. Additionally, we examine the nonexistence of the nontrivial solution of the fractional boundary value problem.