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Ulam’s Type Stability of Delayed Discrete System with Second-Order Differences

  • Maosong Yang [2] ; Michal Feckan [1] ; JinRong Wang [2]
    1. [1] Comenius University

      Comenius University

      Eslovaquia

    2. [2] Guizhou University, Guizhou Open University
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, the Ulam’s type stability of delayed discrete systems with a secondorder difference is investigated. Firstly, we introduce the Hyers–Ulam stability and Hyers–Ulam–Rassias stability concepts for delayed discrete systems with a secondorder difference. Secondly, the uniqueness and existence of the solution of delayed nonlinear discrete systems is proved based on fixed point theory, and the Ulam’s type stability results are presented with the help of the delayed discrete matrix function and discrete Gronwall inequality. Finally, two examples are presented to demonstrate the effectiveness of theoretical results.

  • Referencias bibliográficas
    • 1. Ulam, S.: Problems in Modern Mathematics. Science Editions John Wiley and Sons Inc, New York (1964)
    • 2. Hyers, D.: On the stability of the linear functional equations. Proc. Nat. Acad. Sci. U.S.A. 27(4), 222–224 (1941)
    • 3. Rassias, T.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72(2), 297–300 (1978)
    • 4. Obłoza, M.: Hyers stability of the linear differential equation. Rocznik Nauk.-Dydakt. Prace Mat. 13, 259–270 (1993)
    • 5. Obłoza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Nauk.-Dydakt. Prace Mat. 14,...
    • 6. Rus, I.: Ulam stability of ordinary differential equations. Studia Univ. Babes-Bolyai Math. 4, 125–133 (2009)
    • 7. Wang, J., Feˇckan, M., Zhou, Y.: Ulam’s type stability of impulsive ordinary differential equations. J. Math. Anal. Appl. 395, 258–264...
    • 8. Shah, S.O., Zada, A., Hamza, A.E.: Stability analysis of the first order non-linear impulsive time varying delay dynamic system on time...
    • 9. Shah, S.O., Zada, A.: Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous...
    • 10. Shah, S.O., et al.: Bielecki–Ulam’s types stability analysis of hammerstein and mixed integro-dynamic systems of non-linear form with...
    • 11. Zada, A., Shah, S.O.: Hyers–Ulam stability of firstCorder nonClinear delay differential equations with fractional integrable impulses....
    • 12. Luo, D., Wang, X., Caraballo, T., et al.: Ulam–Hyers stability of Caputo-type fractional fuzzy stochastic differential equations with...
    • 13. Wang, X., Luo, D., Zhu, Q.: Ulam–Hyers stability of caputo type fuzzy fractional differential equations with time-delays. Chaos, Solit....
    • 14. Luo, D., Abdeljawad, T., Luo, Z.: Ulam–Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference...
    • 15. Luo, D., Shah, K., Luo, Z.: On the novel Ulam–Hyers stability for a class of nonlinear Hilfer fractional differential equation with time-varying...
    • 16. Zhao, K.: Stability of a nonlinear fractional Langevin system with nonsingular exponential kernel and delay control. Discrete Dyn. Nat....
    • 17. Zhao, K.: Stability of a nonlinear Langevin system of ML-type fractional derivative affected by timevarying delays and differential feedback...
    • 18. Zhao, K.: Solvability and GUH-stability of a nonlinear CF-fractional coupled Laplacian equations. AIMS Math. 8, 13351–13367 (2023)
    • 19. Zhao, K.: Solvability, approximation and stability of periodic boundary value problem for a nonlinear hadamard fractional differential...
    • 20. Zhao, K.: Generalized UH-stability of a nonlinear fractional coupling (p1, p2)-Laplacian system concerned with nonsingular Atangana-Baleanu...
    • 21. Tripathy, A.: Hyers-Ulam Stability of Ordinary Differential Equations. Taylor and Francis, New York (2021)
    • 22. Popa, D.: Hyers–Ulam–Rassias stability of a linear recurrence. J. Math. Anal. Appl. 309(2), 591–597 (2005)
    • 23. Popa, D.: Hyers–Ulam stability of the linear recurrence with constant coefficients. Adv. Differ. Equ. 2005, 1–7 (2005)
    • 24. Jung, S.: Hyers–Ulam stability of the first order matrix difference equations. Adv. Difference Equ. 2015, 1–13 (2015)
    • 25. Tripathy, A.: Hyers–Ulam stability of second order linear difference equations. Int. J. Differ. Equ. Appl. 16(1), 53–65 (2017)
    • 26. Shen, Y., Li, Y.: The z-transform method for the Ulam stability of linear difference equations with constant coefficients. Adv. Differ....
    • 27. Baias, A., Popa, D.: On Ulam stability of a linear difference equation in Banach spaces. Bull. Malays. Math. Sci. Soc. 43(2), 1357–1371...
    • 28. Dragiˇcevi´c, D.: On the Hyers–Ulam stability of certain nonautonomous and nonlinear difference equations. Aequationes Math. 95(5), 829–840...
    • 29. Anderson, D., Onitsuka, M.: Best constant for Hyers–Ulam stability of second-order h-difference equations with constant coefficients....
    • 30. Anderson, D., Onitsuka, M.: Hyers–Ulam stability and best constant for Cayley h-difference equations. Bull. Malays. Math. Sci. Soc. 43(6),...
    • 31. Anderson, D., Onitsuka, M.: Hyers-Ulam stability for quantum equations of Euler type. Discrete Dyn. Nat. Soc. 2020, (2020)
    • 32. Baias, A., Blaga, F., Popa, D.: Best Ulam constant for a linear difference equation. Carpathian J. Math. 35(1), 13–22 (2019)
    • 33. Jung, M., Nam, W.: Hyers–Ulam stability of Pielou logistic difference equation. J. Nonlinear Sci. Appl. 10, 3115–3122 (2017)
    • 34. Nam, W.: Hyers–Ulam stability of hyperbolic Möbius difference equation. Filomat 32(13), 4555–4575 (2018)
    • 35. Nam, W.: Hyers–Ulam stability of elliptic Möbius difference equation. Cogent Math. Stat. 5(1), 1–9 (2018)
    • 36. Nam, W.: Hyers–Ulam stability of loxodromic Möbius difference equation. Appl. Math. Comput. 356, 119–136 (2019)
    • 37. Zhang, T., Qu, H., Liu, Y., Zhou, J.: Weighted pseudo θ-almost periodic sequence solution and guaranteed cost control for discrete-time...
    • 38. Zhang, T., Li, Z.: Switching clusters’ synchronization for discrete space-time complex dynamical networks via boundary feedback controls....
    • 39. Khusainov, D.Y., Shuklin, G.V.: Linear autonomous time-delay system with permutation matrices solving. Stud. Univ. Žilina 17, 101–108...
    • 40. Diblík, J., Khusainov, D.Y.: Representation of solutions of discrete delayed system x(k+1) = Ax(k)+ Bx(k − m) + f (k)...
    • 41. Diblík, J., Khusainov, D.Y.: Representation of solutions of linear discrete systems with constant coefficients and pure delay. Adv. Differ....
    • 42. Diblík, J., Morávková, B.: Representation of the solutions of linear discrete systems with constant coefficients and two delays. Abstr....
    • 43. Diblík, J., Mencáková, K.: Representation of solutions to delayed linear discrete systems with constant coefficients and with second-order...
    • 44. Diblík, J.: Exponential stability of linear discrete systems with nonconstant matrices and nonconstant delay. AIP Conf. Proc. 1863, 4800031–4800034...
    • 45. Diblík, J., Khusainov, D.Y., R ˚užiˇcková, M.: Exponential stability of linear discrete systems with delay. AIP Conf. Proc. 1978, 4300041–4300044...
    • 46. Baštinec, J., Diblík, J., Khusainov, D.: Stability of linear discrete systems with variable delays. AIP Conf. Proc. 1978, 4300051–4300054...
    • 47. Yang, M., Feˇckan, M., Wang, J.: Relative controllability for delayed linear discrete system with secondorder differences. Qual. Theory...
    • 48. Mahmudov, N., Almatarneh, A.: Stability of Ulam–Hyers and existence of solutions for impulsive time-delay semi-linear systems with non-permutable...
    • 49. Zada, A., Pervaiz, B., Alzabut, J., et al.: Further results on Ulam stability for a system of first-order nonsingular delay differential...
    • 50. Rahmat, G., Ullah, A., Rahman, A., et al.: Hyers–Ulam stability of non-autonomous and nonsingular delay difference equations. Adv. Differ....
    • 51. Moonsuwan, S., Rahmat, G., Ullah, A., et al.: Hyers-Ulam stability, exponential stability, and relative controllability of non-singular...
    • 52. Holte, J.: Discrete Gronwall lemma and applications. In: MAA-NCS meeting at the University of North Dakota 24, 1–7 (2009)
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