  Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix
function and established some properties. The aim of this study established to
devote and derive certain basic properties including analytic properties,
recurrence matrix relations, differential properties, new integral
representations, $k$-Beta transform, Laplace transform, fractional k-Fourier
transform, fractional integral properties, the $k$-Riemann-Liouville and
$k$-Weyl fractional integral and derivative operators an extended version of
$_{r+1}R_{s,k}$ matrix function. We establish its relationships with other well
known special matrix functions which have some particular cases in the context
of three parametric Mittag-Leffer matrix function, $k$-Konhauser and
$k$-Laguerre matrix polynomials. Finally, some special cases of the established
formulas are also discussed.
