Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions

New Lyapunov-type inequalities are derived for the fractional boundary value problem {align*} & D_a^α u(t)+q(t)u(t)=0, a<t<b,\\ &u(a)=u'(a)==u⁽ⁿ⁻²⁾(a)=0, u(b)=I_aα(hu)(b), {align*} where n∈ N, n≥ 2, n-1<α<n, Dₐ^α denotes the Riemann--Liouville fractional derivative of order α, Iₐα denotes the Riemann--Liouville fractional integral of order α, and q,h∈ C([a,b]; R). As an application, we obtain numerical approximations of lower bound for the eigenvalues of corresponding equations.