Abstract
In this paper, by using variational methods, we prove the existence for a class of fractional Hamiltonian systems with Liouville-Weyl fractional derivatives
{lD(alpha)(infinity)((-infinity)D(t)(alpha)u(t) + b(t)u(t) - lambda u(t) = mu f (t,u(t)), t is an element of R u is an element of H-alpha (R)
where alpha is an element of (I /2, I],tD(infinity)(alpha) and D--infinity(t)alpha are the right and left inverse operators of the corresponding Liouville-Weyl fractional integrals of order alpha respectively, u is an element of R, b : R -> R, b is an element of L-infinity(R), inf(t is an element of R)b(t) > 0,lambda,mu are real parameters and f : R x R -> R is a function that satisfies some suitable conditions.