  We consider the initial value problem (IVP) for the fractional Korteweg-de
Vries equation (fKdV) \begin{equation}\label{abstracteq1} \left\{
\begin{array}{ll} \partial_{t}u-D_{x}^{\alpha}\partial_{x}u+u\partial_{x}u=0, &
x,t\in\mathbb{R},\,0<\alpha<1, \\ u(x,0)=u_{0}(x).& \\ \end{array} \right.
\end{equation} It has been shown that the solutions to certain dispersive
equations satisfy the propagation of regularity phenomena. More precisely, it
deals in determine whether regularity of the initial data on the right hand
side of the real line is propagated to the left hand side by the flow solution.
This property was found originally in solutions of Korteweg-de Vries (KdV)
equation and it has been also verified in other dispersive equations as the
Benjamin-Ono (BO) equation.
  Recently, it has been shown that the solutions of the dispersive generalized
Benjamin-Ono (DGBO) equation, this is $\alpha\in (2,3)$ in \eqref{abstracteq1};
also satisfy the propagation of regularity phenomena. This is achieved by
introducing a commutator decomposition to handle the dispersive part in the
equation. Following the approach used in the DGBO, we prove that the solutions
of the fKdV also satisfies the propagation of regularity phenomena.
Consequently, this type of regularity travels with infinite speed to its left
as time evolves.
