  For $0<\alpha<1$ and with initial data $\vert\vert
u_0\vert\vert_{H^{N+\frac{\alpha}{2}}}=\varepsilon$, sufficently small, we show
that the existence time for solutions of the fractional BBM equation
$\partial_tu+\partial_xu+u\partial_xu+\vert\mathrm{D}\vert^\alpha\partial_tu=0$,
can be extended beyond the hyperbolic existence time $\frac{1}{\varepsilon}$,
to $\frac{1}{\varepsilon^2}$. For the proof we use a modified energy, based on
a normal form transformation as in [Hunter, Ifrim, Tataru, Wong, 2015]. In
addition we employ ideas and techniques from [Ehrnstr\"om, Wang, 2018], in
which the authors obtain an enhanced existence time for the fractional KdV
equation.
