Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders (Journal of Nonlinear Modeling and Analysis, 2024)
The paper studies the existence and uniqueness for impulsive fractional $q_k$-difference equations of initial value problems involving Riemann-Liouville fractional $q_k$-integral and $q_k$-derivative by defining a new $q$-shiftingoperator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_k$-difference equations of initial value problems by using theSchaefer’s fixed point theorem and Banach contraction mapping principle. Inaddition, the main result is illustrated with the aid of several examples.