  This paper delves into a novel class of functions defined on an invariant
under translation time scale T, known as (w, c)-periodic functions. This class
encompasses various types of functions, such as periodic, anti-periodic, Bloch,
and unbounded functions. To equip this set of functions with a comprehensive
mathematical framework, we introduce a suitable norm on T, transforming the
space consisting of ({\omega}, c)-periodic functions into a Banach space.
Several fundamental properties of this newly established class are examined.
Furthermore, we present a significant application of our theoretical findings.
We investigate the unique existence of asymptotically exponentially stable (w,
c)-periodic solutions for some families of generalized dynamic equations on
time scales. These dynamic equations represent population models incorporating
feedback and time-varying delays. Our study outlines sufficient conditions for
the emergence of such solutions, highlighting their importance in understanding
the dynamics of complex systems over time scales. In particular, we explore (w,
c)-periodic solutions for prominent models, such as the Nicholsan model,
Lasota- Wazewska model, and their mixed versions on time scales. Our
investigations are groundbreaking, as they encompass both discrete and
continuous cases, presenting a unified perspective on periodic behavior across
various systems.
