  In this paper, we first propose two types of concepts of almost automorphic
functions on the quantum time scale. Secondly, we study some basic properties
of almost automorphic functions on the quantum time scale. Then, we introduce a
transformation between functions defined on the quantum time scale and
functions defined on the set of generalized integer numbers, by using this
transformation we give equivalent definitions of almost automorphic functions
on the quantum time scale. Finally, as an application of our results, we
establish the existence of almost automorphic solutions of linear and
semilinear dynamic equations on the quantum time scale.
