SavedAdd your journal

Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2026 / Cilt: 5 Sayı: 2

Periodic and asymptotically periodic solutions in nonlinear coupled Volterra integro-dynamic systems with infinite delay on time scales

Belkis Bordj(Souk Ahras University)0000-0003-2297-532X
Abdelouaheb Ardjouni(Souk Ahras University)0000-0003-0216-1265
Pages
180–192
Publication Date
2021-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results obtained here extend the work of Raffoul r1 .

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let T be a periodic time scale.
📊
Key Findings & Data:The purpose of this paper is to use Schauder's fixed point theorem to prove the existence of periodic and asymptotically periodic solutions of nonlinear coupled Volterra integro-dynamic systems with infinite delay on time scales.
💡
Conclusion & Impact:The results obtained here extend the work of Raffoul r1 .
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fixed points · periodic solutions · asymptotically periodic solutions

Abstract

Let T be a periodic time scale. The purpose of this paper is to use Schauder's fixed point theorem to prove the existence of periodic and asymptotically periodic solutions of nonlinear coupled Volterra integro-dynamic systems with infinite delay on time scales. The results obtained here extend the work of Raffoul r1 .

🔖

Cite This Article

Bordj, B., Ardjouni, A. (2021). Periodic and asymptotically periodic solutions in nonlinear coupled Volterra integro-dynamic systems with infinite delay on time scales. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 5 Sayı: 2, 180–192. https://doi.org/10.31197/atnaa.691860

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (26)

  1. M. Adivar, H.C. Koyuncuoglu, Y.N. Raffoul, Classification of positive solutions of nonlinear systems of Volterra integrodynamic equations on time scales, Commun. Appl. Anal. 16(3) (2012) 359-375.
  2. M. Adivar, Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations 2009(1) (2009) 1-20.
  3. M. Adivar, Y.N. Raffoul, Existence results for periodic solutions of integro-dynamic equations on time scales, Annali di Matematica 188 (2009) 543-559.
  4. E. Akin, O. Ozturk, On Volterra integro dynamical systems on time scales, Communications in Applied Analysis 23(1) (2019) 21-30.
  5. A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Malaya Journal of Matematik 2(1) (2013) 60-67.
  6. A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52(1) (2013) 5-19.
  7. A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Commun Nonlinear Sci Numer Simulat 17 (2012) 3061-3069.
  8. A. Ardjouni, A. Djoudi, Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale, Rend. Sem. Mat. Univ. Politec. Torino Vol. 68(4)(2010) 349-359.
  9. M. Bohner, A. Peterson, Dynamic equations on time scales, An introduction with applications, Birkhäuser, Boston, (2001).
  10. M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Birkhäuser, Boston, (2003).
  11. F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence and stability of positive periodic solutions for delay nonlinear dynamic equations, Nonlinear Studies 25(1) (2018) 191-202.
  12. F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence of positive solutions of delay dynamic equations, Positivity 21(4) (2017) 1483-1493.
  13. F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for delay dynamic equations, Proyecciones (Antofagasta) 36(3) (2017) 449-460.
  14. J.A. Cid, G. Propst, M. Tvrdy, On the pumping effect in a pipe/tank flow configuration with friction, Physica D: Nonlinear Phenomena 273/274 (2014) 28-33.
  15. I. Culakova, L. Hanustiakova, R. Olach, Existence for positive solutions of second-ordre neutral nonlinear differential equations, Applied Mathematics Letters 22 (2009) 1007-1010.
  16. B. Dorociakova, M. Michalkova, R. Olach, M. Saga, Existence and stability of periodic solution related to valveless pumping, Mathematical Problems in Engineering 2018 (2018) 1-8.
  17. M. Gouasmia, A. Ardjouni, A. Djoudi, Periodic and nonnegative periodic solutions of nonlinear neutral dynamic equations on a time scale, International Journal of Analysis and Applications 16(2) (2018) 162-177.
  18. S. Hilger, Ein Masskettenkalkul mit Anwendung auf Zentrumsmanningfaltigkeiten, PhD thesis, Universitat Wurzburg, (1988).
  19. 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.
  20. V. Lakshmikantham, S. Sivasundaram, B. Kaymarkcalan, Dynamic systems on measure chains, Kluwer Academic Publishers, Dordrecht, (1996).
  21. Z. Li, C. Wang, R.P. Agarwal, D. O'Regan, Commutativity of quaternion-matrix-valued functions and quaternion matrix dynamic equations on time scales, Studies in Applied Mathematics (2020), https://doi.org/10.1111/sapm.12344.
  22. Y.N. Raffoul, Analysis of periodic and asymptotically periodic solutions in nonlinear coupled Volterra integro-differential systems, Turk. J. Math. 42 (2018), 108-120.
  23. D.R. Smart, Fixed points theorems, Cambridge Univ. Press, Cambridge, UK, (1980).
  24. C. Wang, R.P. Agarwal, A classication of time scales and analysis of the general delays on time scales with applications, Mathematical Methods in the Applied Sciences 39(6) (2016) 1568-1590.
  25. C. Wang, R.P. Agarwal, D. O' Regan, R. Sakthivel, Theory of translation closedness for time scales, Developments in Mathematics, Vol. 62, Springer, (2020).
  26. C. Wang, R.P. Agarwal, S. Rathinasamy, Almost periodic oscillations for delay impulsive stochastic Nicholsons blowflies timescale model, Computational and Applied Mathematics 37 (2018) 3005-3026.