In Gao's previous work, the authors determined several graph degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f (x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference ∆ between g(x) and f (x) for every vertex x in G. These obtained new degree conditions reformulate Gao's previous conclusions, and show how ∆ acts in the results. Furthermore, counterexamples are structured to reveal the sharpness of degree conditions in the setting f (x) = g(x) + ∆.