In this paper, new exact and approximate moment generating functions (MGF)expression for generalized fading models are derived. Specifically, we considerthe ${\eta}-{\lambda}-{\mu}$, ${\alpha}-{\mu}$, ${\alpha}-{\eta}-{\mu}$,${\alpha}-{\lambda}-{\mu}$, ${\alpha}-{\kappa}-{\mu}$, and${\alpha}-{\lambda}-{\eta}-{\mu}$ generalized fading distributions to deriveapproximate MGF expressions. The new expressions are very accurate and, incontrast to earlier results in the literature, avoid any complicated specialfunctions, e.g. the Meijer-$G$ and Fox $H$-functions. As such, the new MGFexpressions allow easier and more efficient analytical manipulations, whichalso apply for their special cases such as the Rayleigh, Rice, and Nakagami-mfading. As an illustrative application, the average bit error rates for each ofthe fading models are evaluated using the new derived MGF expressions. Theaccuracy of the analytical results by using the numerically computed results asa basis of comparison as well as published results from the literature.
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