A graph
![$G$](img33.png)
is called fractional
![$(a,b,k)$](img52.png)
-critical covered if
![$G-Q$](img53.png)
is fractional
![$[a,b]$](img54.png)
-covered for any
![$Q\subseteq V(G)$](img55.png)
with
![$\vert Q\vert=k$](img56.png)
. In this article, we demonstrate an
independence number and minimum degree condition for a graph to be fractional
![$(a,b,k)$](img52.png)
-critical
covered, which is a generalization of Zhou's previous result [S. Zhou, Some new sufficient
conditions for graphs to have fractional
![$k$](img57.png)
-factors, International Journal of Computer
Mathematics 88(3)(2011)484-490]. Furthermore, we demonstrate that two conditions on independence
number and minimum degree in our main result are sharp.