  In recent years, the Boussinesq type fractional partial differential equation
has attracted much attentions of researchers for its practical importance. In
this paper we study a non-local problem for the Boussinesq type equation
$D_t^\alpha u(t)+A D_t^\alpha u(t)+\nu^2A u(t)=0,\,\, 0< t< T,\,\, 1<\alpha<2,$
where $D_t^\alpha$ is the Caputo fractional derivative and $A$ is abstract
operator. In the classical case, i.e. at $\alpha=2$, this problem was studied
earlier and an interesting effect was discovered: the well-posedness of the
problem significantly depends on the length of the time interval and the
parameter $\nu$. This note shows that for the case of a fractional equation
there is no such effect: the problem is well-posed for any $T$ and $\nu$.
