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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

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Mathematical Citation Quotient (MCQ) 2016: 0.56


Emerging Science

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2353-0626
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Periodicity, almost periodicity for time scales and related functions

Chao Wang
  • Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People’s Republic of China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Ravi P. Agarwal
  • Department of Mathematics, Texas A&M University-Kingsville, TX 78363-8202, Kingsville, TX, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Donal O’Regan
  • School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-05-30 | DOI: https://doi.org/10.1515/msds-2016-0003

Abstract

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

Keywords: Time scales; Almost periodic time scales; Changing periodic time scales

References

  • [1] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston Inc., Boston, 2001. Google Scholar

  • [2] C.Wang, R.P. Agarwal, Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy, Adv. Differ. Equ., 296 (2015) 1-21. CrossrefWeb of ScienceGoogle Scholar

  • [3] C. Wang, Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014) 2828-2842. Web of ScienceGoogle Scholar

  • [4] C. Wang, R.P. Agarwal, A classification of time scales and analysis of the general delays on time scales with applications, Math. Meth. Appl. Sci., 39 (2016) 1568-1590. Web of ScienceGoogle Scholar

  • [5] C. Wang, R.P. Agarwal, Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive ∆- dynamic system on time scales, Appl. Math. Comput., 259 (2015) 271-292. Web of ScienceGoogle Scholar

  • [6] C. Wang, R.P. Agarwal, A further study of almost periodic time scales with some notes and applications, Abstr. Appl. Anal., (2014) 1-11 (Article ID 267384). Google Scholar

  • [7] E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl., 319 (2006) 315-325. Google Scholar

  • [8] Y. Li, C.Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., (2011). 22p (Article ID 341520). Google Scholar

  • [9] M. Adıvar, A new periodicity concept for time scales, Math. Slovaca, 63 (2013) 817-828. Web of ScienceGoogle Scholar

  • [10] C. Wang, R.P. Agarwal, Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations, Adv. Differ. Equ., 312 (2015) 1-9. CrossrefGoogle Scholar

  • [11] A. Wilansky, Topics in Functional Analysis, Springer, Lecture Notes in Mathematics, Volume 45 (1967). Google Scholar

  • [12] Y. Li, B. Li, Almost periodic time scales and almost periodic functions on time scales, J. Appl. Math., (2015) 1-8 (Article ID 730672). Google Scholar

  • [13] B. Sendov, Hausdorff Approximations, Kluwer Academic Publishers, Netherlands, (1990). Google Scholar

About the article

Received: 2015-12-09

Accepted: 2016-05-04

Published Online: 2016-05-30


Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2016-0003.

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©2016 Chao Wang et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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