Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2026 04 15 Ground state solutions for two classes of fractional Hamiltonian systems 10559 10.22075/ijnaa.2025.28026.3784 EN Mohsen Timoumi Dpt of Mathematics, Faculty of Sciences of Monastir, 5000 Monastir, Tunisia 0000-0003-1350-7110 Journal Article 2022 08 06 In this paper, we are concerned with the following periodic fractional Hamiltonian system<br />$$\left\{<br />\begin{array}{l}<br />_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in\mathbb{R}\\<br />u\in H^{\alpha}(\mathbb{R}).<br />\end{array}\right.$$<br />Using variational methods and a version of the concentration compactness principle, we study the existence of ground state solutions for this system under two different classes of superquadratic conditions weaker than the ones known in the literature. To the best of our knowledge, there has been no work focused in this case. Fractional Hamiltonian systems ground state orbits periodic potentials Variational methods concentration compactness principle https://ijnaa.semnan.ac.ir/article_10559_7a20fd764fa23d34b52bd85bf5cb49a6.pdf