This paper addresses the mobility control (MC) for Device to Device (D2D) in downlink multi-cell OFDMA system with cooperative relaying and Fractional Frequency Reuse (FFR) scheme. D2D equipments are characterized by limited capacity of battery and suffer from Co-Channel Interference (CCI) at cell edge. FFR and cooperative relaying schemes are proposed to improve energy efficiency (EE) and avoid CCI. In the edge region, according to a difference set and using the sectorization technique, the FFR of 7/3 and 7/4 have been applied. The deployment of FFR with Amplify and Forward (AF) fixed relays improve significantly the system performance of Frequency Reuse Factor (FRF) of 1 and 3.