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In this paper, we study a quantum difference coupled impulsive system with respect to another function. Some quantum derivative and integral asymmetric graphs with respect to another function are shown to illustrate the behavior of parameters. Existence and uniqueness results are established via Banach contraction mapping principle and Leray–Schauder alternative. Examples illustrating the obtained results are also included. Our results are new and significantly contribute to the literature to this new subject on quantum calculus on finite intervals with respect to another function. [ABSTRACT FROM AUTHOR]