Title: Pseudo periodicity and pseudo almost periodicity in shifts δ_± on time scales

Authors: Meng Hu; Lili Wang

Addresses: School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan – 455000, China ' School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan – 455000, China

Abstract: By means of the shifts operators δ_±, we first define the concepts of pseudo (v-pseudo) periodic function in shifts δ_± and pseudo (v-pseudo) almost periodic function in shifts δ_± on time scales, then by using the calculus on time scales and the properties of the shift operators δ_±, the existence and uniqueness theorems of pseudo (v-pseudo) periodic solution in shifts δ_± and pseudo (v-pseudo) almost periodic solution in shifts δ_± of a linear dynamic equation are established, respectively. Finally, two delayed dynamic equations are studied on some specific time scales, the corresponding examples are given to illustrate the usefulness of our results.

Keywords: pseudo periodicity; pseudo almost periodicity; shift operator; time scale.

DOI: 10.1504/IJDSDE.2024.144872

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.4, pp.323 - 338

Received: 26 Mar 2023
Accepted: 11 Oct 2023
Published online: 06 Mar 2025 *