Under the generalized weak convexity of (F, d , , ρ α ), we studied the results of several sorts of duality type about the problem of multi-objective fractional programming (MFP), extended this results to the generalized arcwise connected hypothesis, established the optimized problem of arcwise connected area (ACP) and the optimal sufficient condition of under constraint condition, and gave the duality model, and obtained the conclusions of weak duality and strong duality.