Wireless power transfer and energy harvesting have attracted a significant research attention in terms of their application in cooperative relaying systems. Most of existing works in this field focus on the half-duplex (HD) relaying mechanism over certain fading channels, however, in contrast, this paper considers a dual-hop full-duplex (FD) relaying system over a generalized independent but not identically distributed α-μfading channel, where the relay node is energy-constrained and entirely depends on the energy signal from the source node. Three special cases of the α-μmodel are investigated, namely, Rayleigh, Nakagami-m and Weibull fading. As the system performance, we investigate the outage probability (OP) for which we derive exact unified closed-form expressions. The provided Monte Carlo simulations validate the accuracy of our analysis. Moreover, the results obtained for the FD scenario are compared to the ones related to the HD. The results demonstrate that the decode-andforward relaying outperforms the amplify-and-forward relaying for both HD and FD scenarios. It is also shown that the FD scenario performs better than the HD relaying systems. Finally, we analyzed the impact of the fading parameters αand μon the achievable OP.