(untitled) (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-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional q_k-difference equations of initial value problems by using the Schaefer’s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples.