文摘
This paper studies a Caputo type anti-periodic boundary value problem of impulsive fractional q-difference equations involving a q-shifting operator of the form \({}_{a}\Phi_{q}(m) = qm + (1-q)a\). Concerning the existence of solutions for the given problem, two theorems are proved via Schauder’s fixed point theorem and the Leray-Schauder nonlinear alternative, while the uniqueness of solutions is established by means of Banach’s contraction mapping principle. Finally, we discuss some examples illustrating the main results. Keywords quantum calculus impulsive fractional q-difference equations existence uniqueness fixed point theorem