-order -almost periodic functions and dynamic equations

In this paper, using matched spaces for time scales, we introduce new types of almost periodic functions, including δ -almost periodic functions and n₀-orderΔ -almost periodic functions (Δ^δ _n0 -almost periodic functions). Also we introduce the definition of hull equations for homogeneous dynamic equations and obtain some existence results. Under exponential dichotomy for the corresponding homogeneous equation, we obtain the form of a δ -almost periodic solution with the Δ^δ _n0 -almost periodic affiliated function for a type of nonhomogeneous dynamic equation and we use it to study the existence of δ -almost periodic solutions with the Δ^δ _n0-almost periodic affiliated function for new delay dynamic equations.