The bipartite consensus of fractional multi-agent systems with delay under fixed and switching topologies is addressed in the article. First, for a fixed topology, a delayed control protocol is developed and several feasible conditions of bipartite consensus are proposed with the help of fractional-order Razumikhin theory and signed graph theory. Secondly, regarding the switching topologies, the bipartite consensus is further investigated by the aid of common Lyapunov function method. The proposed way can commendably surmount the trouble arising from time delay, fractional-order derivative and switchings. Ultimately, the feasibility of theoretical conclusions is verified though two simple examples.