Multiple solutions for a class of superquadratic fractional Hamiltonian systems

In this paper, we are concerned with the existence of solutions for a class of fractional Hamiltonian systems \[\left\{ \begin{array}{l} _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in\mathbb{R}\\ u\in H^{\alpha}(\mathbb{R},\ \mathbb{R}^{N}), \end{array}\right. \] where $_{t}D_{\infty}^{\alpha}$ and $_{-\infty}D^{\alpha}_{t}$ are the Liouville-Weyl fractional derivatives of order $\frac{1}{2}