  Our present investigation is mainly based on the $k$-hypergeometric functions
which are constructed by making use of the Pochhammer $k$-symbol \cite{Diaz}
which are one of the vital generalization of hypergeometric functions. We
introduce $k$-analogues of $F_{2}\ $and $F_{3}$ Appell functions denoted by the
symbols $F_{2,k}\ $and $F_{3,k}\ $respectively, just like Mubeen et al. did for
$F_{1}$ in 2015 \cite{Mubeen6}. Meanwhile, we prove some main properties namely
integral representations, transformation formulas and some reduction formulas
which help us to have relations between not only $k$-Appell functions but also
$k$-hypergeometric functions. Finally, employing the theory of Riemann
Liouville $k$-fractional derivative \cite{Rahman} and using the relations which
we consider in this paper, we acquire linear and bilinear generating relations
for $k$-analogue of hypergeometric functions and Appell functions.
