TY - JOUR
T1 - Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_k$-Difference Equations for Impulsive with Varying Orders
AU - Zhang , Lulu
AU - Li , Fanjun
AU - Han , Zhenlai
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 701
EP - 721
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.701
UR - https://global-sci.org/intro/article_detail/jnma/21907.html
KW - Impulsive fractional $q_k$-difference equation, Boundary value problem, Existence, Uniqueness.
AB - <p style="text-align: justify;">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.</p>