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

Abstract

New Lyapunov-type inequalities are derived for the fractional boundary value problem Daa u(t) + q(t)u(t) = 0, a <t <b, u(a) = u0(a) = … = u(n-2)(a) = 0, u(b) = Iaa (hu)(b), where n E IN, n > 2, n - 1 < <n, Daa denotes the Riemann–Liouville fractional derivative of order a, Iaa denotes the Riemann–Liouville fractional integral of order a, and q, h 2 C([a, b];R). As an application, we obtain numerical approximations of lower bound for the eigenvalues of corresponding equations