Geodesic
Existence of solutions for fractional Hamiltonian systems
Electronic journal of differential equations, Tome 2013 (2013)
In this work we prove the existence of solutions for the fractional differential equation

$ _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) + L(t)u(t) = \nabla W(t,u(t)),\quad u\in H^{\alpha}(\mathbb{R}, \mathbb{R}^{N}). $

where $\alpha \in (1/2, 1)$. Assuming L is coercive at infinity we show that this equation has at least one nontrivial solution.
Classification : 26A33, 34C37, 35A15, 35B38
Keywords: Liouville-Weyl fractional derivative, fractional Hamiltonian systems, critical point, variational methods 
@article{EJDE_2013__2013__a59,
     author = {Torres,  Cesar},
     title = {Existence of solutions for fractional {Hamiltonian} systems},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1295.34012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a59/}
}
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%J Electronic journal of differential equations
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Torres,  Cesar. Existence of solutions for fractional Hamiltonian systems. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a59/