A new periodicity concept for time scales

By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition: “there exists a $P>0$ such that $t\pm P\in \mathbb{T}$ for all $t\in \mathbb{T}$”, unlike the existing literature. Therefore, the results of this paper open an avenue for the investigation of periodic solutions of $q$-difference equations.