Quantum calculus on finite intervals and applications to impulsive difference equations

Abstract

In this paper we initiate the study of quantum calculus on finite intervals. We define the qk-derivative and qk-integral of a function and prove their basic properties. As an application, we prove existence and uniqueness results for initial value problems for first- and second-order impulsive qk-difference equations. ©2013 Tariboon and Ntouyas; licensee Springer.