We study the existence of solutions for the following fractional Hamiltonian systems (Formula Presented) where α ∈ (1/2, 1), t ∈ ℝ, u ∈ ℝn, λ > 0 is a parameter, L ∈ C(ℝ, ℝn2 ) is a symmetric matrix, W ∈ C1 (ℝ × ℝn, ℝ). Assuming that L(t) is a positive semi-definite symmetric matrix, that is, L(t) ≡ 0 is allowed to occur in some finite interval T of ℝ, W (t, u) satisfies some superquadratic conditions weaker than Ambrosetti-Rabinowitz condition, we show that (FHS)λ has a solution which vanishes on ℝ \ T as λ → ∞, and converges to some ũ ∈ Hα (ℝ, ℝn). Here, ũ ∈ E0α is a solution of the Dirichlet BVP for fractional systems on the finite interval T. Our results are new and improve recent results in the literature even in the case α = 1.