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In this work we study the existence of solution for a class of fractionaldifferential equation given by \begin{eqnarray}\label{eq00}_{t}D_{\infty}^{\alpha}{_{-\infty}}D_{t}^{\alpha}u(t) + u(t) = & f(t,u(t))\\u\in H^{\alpha}(\mathbb{R}).\nonumber \end{eqnarray} where $\alpha \in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}$, $f\in C(\mathbb{R}, \mathbb{R})$.Using mountain pass theorem and comparison argument we prove that (\ref{eq00})at least has one nontrivial solution.

Ground state solution for a class of differential equations with left and right fractional derivatives