  In this work we establish the formation of singularities of classical
solutions with finite energy of the forced fractional Navier Stokes equations
where the dissipative term is given by $|\nabla|^{\alpha}$ for any $\alpha\in
[0, \alpha_0)$ ($\alpha_0 = \frac{22-8\sqrt7}{9} > 0$). We construct solutions
in $\mathbb{R}^3\times [0,T]$ with a finite $T>0$ and with an external forcing
which is in $L^1_t([0, T]) C_x^{1,\epsilon}\cap L^{\infty}_{t}L_{x}^2$, such
that on the time interval $0 \le t < T$, the velocity $u$ is in the space
$C^\infty\cap L^2$ and such that as the time $t$ approaches the blow-up moment
$T$, the integral $\int_0^t |\nabla u| ds$ tends to infinity.
