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Our present investigation is mainly based on the $k$-hypergeometric functionswhich are constructed by making use of the Pochhammer $k$-symbol \cite{Diaz}which are one of the vital generalization of hypergeometric functions. Weintroduce $k$-analogues of $F_{2}\ $and $F_{3}$ Appell functions denoted by thesymbols $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 namelyintegral representations, transformation formulas and some reduction formulaswhich help us to have relations between not only $k$-Appell functions but also$k$-hypergeometric functions. Finally, employing the theory of RiemannLiouville $k$-fractional derivative \cite{Rahman} and using the relations whichwe consider in this paper, we acquire linear and bilinear generating relationsfor $k$-analogue of hypergeometric functions and Appell functions.

On some formulas for the $k$-analogue of Appell functions and generating relations via $k$-fractional derivative