δ-almost periodic functions and applications to dynamic equations

In this paper, by employing matched spaces for time scales, we introduce a δ-almost periodic function and obtain some related properties. Also the hull equation for homogeneous dynamic equation is introduced and results of the existence are presented. In the sense of admitting exponential dichotomy for the homogeneous equation, the expression of a δ-almost periodic solution for a type of nonhomogeneous dynamic equation is obtained and the existence of δ-almost periodic solutions for new delay dynamic equations is considered. The results in this paper are valid for delay q-difference equations and delay dynamic equations whose delays may be completely separated from the time scale T.