Almost Periodicity on Isolated Time Scales and Applications

ABSTRACT In this work, we formulate a generalized definition of almost periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. We state two different definitions of almost periodicity and we show their relation. Moreover, we establish fundamental properties for this class of functions, along with the conditions for the existence of almost periodic solutions for a family of first‐order linear dynamic equations. Many examples in quantum calculus and other kinds of isolated time scales are given.