This paper investigates the fundmental bifurcations for the fractional differential systems involving one parameter in the variable space. Applying the Lyapunov direct method to the fractional differential systems to prove the stability or the instability of the equilibria, the phase portraits of the bifurcations are obtained. With the help of the Taylor's expansion and the Implicit Function Theorem in the classical sense, the normal forms of the bifurcations of the fractional differential systems are calculated. By using the topological equivalent map which depend on one parameter, the topological normal forms of the bifurcations of the fractional differential systems are derived.