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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-μ fading 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-μ model 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 …