δ-Almost Periodic Functions and Applications to Dynamic Equations

Abstract

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.

A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales

“…([ 36 , 38 , 39 ]) . A function is δ-almost periodic in t uniformly for under the matched space if and only if for every pair of sequences , there exist common subsequences such that …”

Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

“…On the other hand, in 1988, Stefan Hilger introduced the theory of time scales, which is a powerful tool to study dynamic equations on hybrid domains (see [9]), by choosing the time scale to be the set of real numbers, the general results yield the results concerning different types of dynamic equations (see [20,23,27]). In 2016, some equivalent concepts of periodic time scales were addressed by Wang and Agarwal et al(see [2,21,22]).…”