In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional (Formula presented.) -difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii’s fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work.