  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.
