  We propose a non-minimally coupled gravity model in $ Y(R)F^2 $ form to
describe the radiation fluid stars which have the radiative equation of state
between the energy density $ \rho $ and the pressure $p$ as $\rho=3p $. Here
$F^2$ is the Maxwell invariant and $Y(R)$ is a function of the Ricci scalar
$R$. We give the gravitational and electromagnetic field equations in
differential form notation taking the infinitesimal variations of the model. We
look for electrically charged star solutions to the field equations under a
constraint which eliminating complexity of the higher order terms in the field
equations. We determine the non-minimally coupled function $Y(R)$ and the
corresponding model which admits new exact solutions in the interior of star
and Reissner-Nordstrom solution at the exterior region. Using vanishing
pressure condition at the boundary together with the continuity conditions of
the metric functions and the electric charge, we find the mass-radius ratio,
charge-radius ratio and gravitational surface redshift depending on the
parameter of the model for the radiation fluid star. We derive general
restrictions for the ratios and redshift of the charged compact stars. We
obtain a slightly smaller upper mass-radius ratio limit than the Buchdahl bound
$ 4/9 $ and a smaller upper redshift limit than the bound of the standard
General Relativistic stars.
