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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]

In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of (k;φ')-Hilfer fractional differential equations supplemented with nonlocal integromulti- point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'skii's fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters β1; β2; and the function φ involved in the problem at hand. [ABSTRACT FROM AUTHOR]