In this paper we are concerned with the existence of solutions for the following fractional Hamiltonian systems with a parameter (Formula presented.) where α∈ (1 / 2 , 1), t∈ R, u∈ Rn, λ> 0 is a parameter, L∈C(R,Rn2) is a symmetric matrix for all t∈ R, W∈ C1(R× Rn, R) and ∇ W(t, u) is the gradient of W(t, u) at u. The novelty of this paper is that, assuming L(t) is a symmetric and positive semi-definite matrix for all t∈ R, that is, L(t) ≡ 0 is allowed to occur in some finite interval T of R, W(t, u) satisfies Ambrosetti–Rabinowitz condition and some other reasonable hypotheses, we show the existence of nontrivial solution of (FHS)λ, which vanishes on R\ T as λ→ ∞, and converges to u~ ∈ Hα(R) ; here u~∈E0α is a nontrivial solution of the Dirichlet BVP for fractional systems on the finite interval T. Recent results are generalized and significantly improved.