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In the present contribution, we propose a comprehensive framework for the analysis of cooperative dual-hop wireless systems over generalized fading channels, which use an amplify and forward (AF) relaying mechanism with blind and semi-blind relays. In particular, the proposed framework provides either exact results or very accurate bounds for computing the moment generating function (MGF) of the end-to-end signal-to-noise ratio (SNR) for various fading channel models typically encountered in real propagation environments. Furthermore, with the help of the MGF-based approach for performance analysis of wireless systems over fading channels, we will show that important performance indexes can be easily derived from the MGF. With respect to previous published articles on the matter, the main contribution of the paper is twofold: i) by relying on the properties of the Meijer-G function, either exact expressions or accurate bounds for the MGF of the end-to-end SNR are provided, and ii) the analysis encompasses the vast majority of fading channel models. Numerical and simulation results will be compared to substantiate the analytical derivation.