  The aim of this paper is to obtain the existence of solution for the
fractional p-Laplacian Dirichlet problem with mixed derivatives
\begin{eqnarray*}
&{_{t}}D_{T}^{\alpha}\left(|_{0}D_{t}^{\alpha}u(t))|^{p-2}{_{0}}D_{t}^{\alpha}u(t)\right)
= f(t,u(t)), \;t\in [0,T],\\ &u(0) = u(T) = 0, \end{eqnarray*} where
$\frac{1}{p} < \alpha <1$, $1<p<\infty$ and $f:[0,T]\times \mathbb{R} \to
\mathbb{R}$ is a Carath\'eodory function wich satisfies some growth conditions.
We obtain the existence of nontrivial solution by using the Mountain Pass
Theorem.
