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In this paper, we introduce new concepts of Hahn difference operator, the qk,ωk$q_{k},\omega_{k}$-Hahn difference operator. We aim to establish a calculus of differences based on the qk,ωk$q_{k},\omega_{k}$-Hahn difference operator. We construct a right inverse of the qk,ωk$q_{k},\omega_{k}$-Hahn operator and study some of its properties. As applications, we establish existence and uniqueness results for first- and second-order impulsive qk,ωk$q_{k},\omega_{k}$-Hahn difference equations.

New concepts of Hahn calculus and impulsive Hahn difference equations