  This work is devoted to the formulation and derivation of the
$\alpha{-}\kappa{-}\mu{/}$gamma distribution which corresponds to a physical
fading model. The proposed distribution is composite and is constituted by the
$\alpha{-}\kappa{-}\mu$ non-linear generalized multipath model and the gamma
shadowing model. It also constitute the basis for deriving the
$\alpha{-}\kappa{-}\mu$ \textit{Extreme}${/}$gamma model which accounts for
non-linear severe multipath and shadowing effects and also includes the more
widely known $\alpha{-}\mu$ and $\kappa{-}\mu$ models which includes as special
cases the Rice, Weibull, Nakagami-$m$ and Rayleigh distributions. The derived
models provide accurate characterisation of the simultaneous occurrence of
multipath fading and shadowing effects. This is achieved thanks to the
remarkable flexibility of their named parameters which have been shown to
render them capable of providing good fittings to experimental data associated
with realistic communication scenarios. This is also evident by the fact that
they include as special cases the widely known composite fading models such as
the recently reported $\kappa{-}\mu{/}$gamma model and the novel
$\alpha{-}\mu{/}$gamma model. Novel analytic expressions are derived for the
corresponding probability density function of these distributions which are
expressed in a convenient algebraic form and can be efficiently utilized in the
derivation of numerous vital measures in investigations related to the analytic
performance evaluation of digital communications over composite
multipath${/}$shadowing fading channels.
