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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.