  This paper presents a somewhat exhaustive study on the conformable fractional
Gauss hypergeometric function (CFGHF). We start by solving the conformable
fractional Gauss hypergeometric equation (CFGHE) about the fractional regular
singular points $x=1$ and $x=\infty$. Next, various generating functions of the
CFGHF are established. We also develop some differential forms for the CFGHF.
Subsequently, differential operators and the contiguous relations are reported.
Furthermore, we introduce the conformable fractional integral representation
and the fractional Laplace transform of CFGHF. As an application, and after
making a suitable change of the independent variable, we provide general
solutions of some known conformable fractional differential equations, which
could be written by means of the CFGHF.
