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We consider the initial value problem (IVP) for the fractional Korteweg-deVries 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 dispersiveequations satisfy the propagation of regularity phenomena. More precisely, itdeals in determine whether regularity of the initial data on the right handside 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 theBenjamin-Ono (BO) equation.  Recently, it has been shown that the solutions of the dispersive generalizedBenjamin-Ono (DGBO) equation, this is $\alpha\in (2,3)$ in \eqref{abstracteq1};also satisfy the propagation of regularity phenomena. This is achieved byintroducing a commutator decomposition to handle the dispersive part in theequation. Following the approach used in the DGBO, we prove that the solutionsof the fKdV also satisfies the propagation of regularity phenomena.Consequently, this type of regularity travels with infinite speed to its leftas time evolves.

On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation