In this paper, we prove the existence of infinitely many solutions for the following nonperiodic fractional Hamiltonian system

where \(_{-\infty }D_{t}^{\alpha }\) and \(_{t}D^{\alpha }_{\infty }\) are left and right Liouville–Weyl fractional derivatives of order \(\frac{1}{2}<\alpha <1\) on the whole axis, respectively, \(L\in C({\mathbb {R}},{\mathbb {R}}^{N^{2}})\) is a symmetric matrix valued function unnecessary coercive and \(W(t,x)\in C^{1}({\mathbb {R}}\times {\mathbb {R}}^{N},{\mathbb {R}})\) is only locally defined and superquadratic near the origin with respect to x. Our results extend and improve some existing results in the literature.

在本文中，我们证明了以下非周期分数哈密顿系统的无穷多解的存在性

其中\(_{-\infty }D_{t}^{\alpha }\)和\(_{t}D^{\alpha }_{\infty }\)是左和右 Liouville-Weyl 分数阶导数在整个轴上排列\(\frac{1}{2}<\alpha <1\)，分别为\(L\in C({\mathbb {R}},{\mathbb {R}}^{N ^{2}})\)是对称矩阵值函数不必要的强制和\(W(t,x)\in C^{1}({\mathbb {R}}\times {\mathbb {R}}^ {N},{\mathbb {R}})\)仅在原点附近关于x是局部定义的和超二次的。我们的结果扩展和改进了文献中的一些现有结果。