We consider the area A=\int_0^{\infty}\left(\sum_{i=1}^{\infty}
X_i(t)\right) \d t of a self-similar fragmentation process \X=(\X(t), t\geq
0) with negative index. We characterize the law of A by an
integro-differential equation. The latter may be viewed as the infinitesimal
version of a recursive distribution equation that arises naturally in this
setting. In the case of binary splitting, this yields a recursive formula for
the entire moments of A which generalizes known results for the area of the
Brownian excursion
