Abstract
A Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem
(D-C(a)alpha,psi u) (x) + f (x, u(x)) = 0, a < x < b,
u(a) + u(b) = 0, u'(a) + u'(b) = 0,
where (a, b) is an element of R-2, a < b, 1 < alpha < 2, psi C-2([a, b]), psi' (x) > 0, x is an element of[a, b], D-C(a)alpha,psi is the psi-Caputo fractional derivative of order alpha, and f : [a, b] x R -> R is a given function. Next, we give an application of the obtained inequality to the corresponding eigenvalue problem.