Ir al contenido

Documat

Bielecki–Ulam’s Types Stability Analysis of Hammerstein and Mixed Integro–Dynamic Systems of Non–Linear Form with Instantaneous Impulses on Time Scales

  • Syed Omar Shah [1] ; Cemil Tunç [3] ; Rizwan Rizwan [4] ; Akbar Zada [2] ; Qayyum Ullah Khan [1] ; Iftikhar Ullah [1] ; Ibrar Ullah [1]
    1. [1] Qurtuba University of Science and Information Technology

      Qurtuba University of Science and Information Technology

      Pakistán

    2. [2] University of Peshawar

      University of Peshawar

      Pakistán

    3. [3] Van Yuzuncu Yil University
    4. [4] University of Buner
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, the stability in terms of Bielecki–Ulam–Hyers and stability in terms of Bielecki–Ulam–Hyers–Rassias of non–linear impulsive Hammerstein integro– dynamic system with delay and non–linear impulsive mixed integro–dynamic system on time scales are achieved by utilizing fixed point approach along with Lipschitz condition and Gronwall’s inequality. Examples are also provided for the verification of the results.

  • Referencias bibliográficas
    • 1. Agarwal, R.P., Awan, A.S., ÓRegan, D., Younus, A.: Linear impulsive Volterra integro-dynamic system on time scales. Adv. Differ. Equ. 2014(6),...
    • 2. Alsina, C., Ger, R.: On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2, 373–380 (1998)
    • 3. Alzabut, J.O., Mohammadaliee, B., Samei, M.E.: Solutions of two fractional q-integro-differential equations under sum and integral boundary...
    • 4. András, S., Mészáros, A.R.: Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219(9),...
    • 5. Bainov, D.D., Dishliev, A.: Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken...
    • 6. Bainov, D.D., Simenov, P.S.: Systems with impulse effect stability theory and applications. Ellis Horwood Limited, Chichester, UK (1989)
    • 7. Bohner, M., Li, T.: Kamenev-type criteria for nonlinear damped dynamic equations. Sci. China Math. 58(7), 1445–1452 (2015)
    • 8. Bohner, M., Peterson, A.: Dynamic equations on time scales: an introduction with applications. Birkhäuser, Boston, Mass, USA (2001)
    • 9. Bohner, M., Peterson, A.: Advances in dynamics equations on time scales. Birkhäuser, Boston, Mass, USA (2003)
    • 10. Dachunha, J.J.: Stability for time varying linear dynamic systems on time scales. J. Comput. Appl. Math. 176(2), 381–410 (2005)
    • 11. Georgieva, A., Kostadinov, S., Stamov, G.T., Alzabut, J.O.: On L p(k)-equivalence of impulsive differential equations and its applications...
    • 12. Hamza, A., Oraby, K.M.: Stability of abstract dynamic equations on time scales. Adv. Differ. Equ. 2012(143), 1–15 (2012)
    • 13. Hilger, S.: Analysis on measure chains-A unified approach to continuous and discrete calculus. Result Math. 18, 18–56 (1990)
    • 14. Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A. 27(4), 222–224 (1941)
    • 15. Jung, S.-M.: Hyers-Ulam stability of linear differential equations of first order. Appl. Math. Lett. 17(10), 1135–1140 (2004)
    • 16. Jung, S.-M.: Hyers–Ulam–Rassias stability of functional equations in nonlinear analysis, Springer Optim. Appl., Springer, NewYork, 48,...
    • 17. Li, T., Pintus, N., Viglialoro, G.: Properties of solutions to porous medium problems with different sources and boundary conditions....
    • 18. Li, Y., Shen, Y.: Hyers-Ulam stability of linear differential equations of second order. Appl. Math. Lett. 23(3), 306–309 (2010)
    • 19. Li, T., Viglialoro, G.: Boundedness for a nonlocal reaction chemotaxis model even in the attractiondominated regime. Differ. Integral...
    • 20. Li, T., Zada, A.: Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded...
    • 21. Lupulescu, V., Zada, A.: Linear impulsive dynamic systems on time scales. Electron. J. Qual. Theory Differ. Equ. (11), 1–30 (2010)
    • 22. Marras, M., Viglialoro, G.: Blow-up time of a general Keller-Segel system with source and damping terms. Comptes Rendus de L’Academie...
    • 23. Nenov, S.I.: Impulsive controllability and optimization problems in population dynamics. Nonlinear Anal. Theory Methods Appl. 36(7), 881–890...
    • 24. Obłoza, M.: Hyers stability of the linear differential equation. Rocznik Nauk.-Dydakt. Prace Mat. (13), 259–270 (1993)
    • 25. Obłoza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Nauk.-Dydakt. Prace Mat....
    • 26. Pötzsche, C., Siegmund, S., Wirth, F.: A spectral characterization of exponential stability for linear time-invariant systems on time...
    • 27. Pratap, A., Raja, R., Alzabut, J.O., Cao, J., Rajchakit, G., Huang, C.: Mittag-Leffler stability and adaptive impulsive synchronization...
    • 28. Qiu, Y.-C., Zada, A., Tang, S., Li, T.: Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time...
    • 29. Rassias, T.M.: On the stability of linear mappings in Banach spaces. Proc. Amer. Math. Soc. 72(2), 297–300 (1978)
    • 30. Saker, S.H., Alzabut, J.O.: On the impulsive delay Hematopoiesis model with periodic coefficients. Rocky. Mt. J. Math. 39(5), 1657–1688...
    • 31. Senthilraj, S., Saravanakumar, T., Raja, R., Alzabut, J.O.: Delay-dependent passivity analysis of nondeterministic genetic regulatory...
    • 32. Shah, S.O., Zada, A.: On the stability analysis of non-linear Hammerstein impulsive integro-dynamic system on time scales with delay....
    • 33. Shah, S.O., Zada, A.: Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous...
    • 34. Shah, S.O., Zada, A., Hamza, A.E.: Stability analysis of the first order non-linear impulsive time varying delay dynamic system on time...
    • 39. Ulam, S.M.: Problem in modern mathematics, Science Editions. J. Wiley and Sons Inc, New York (1964)
    • 40. Vinodkumar, A., Senthilkumar, T., Hariharan, S., Alzabut, J.O.: Exponential stabilization of fixed and random time impulsive delay differential...
    • 41. Wang, J.R., Feˇckan, M., Tian, Y.: Stability analysis for a general class of non-instantaneous impulsive differential equations. Mediterr....
    • 42. Wang, J.R., Feˇckan, M., Zhou, Y.: Ulam’s type stability of impulsive ordinary differential equations. J. Math. Anal. Appl. 395(1), 258–264...
    • 43. Wang, J.R., Feˇckan, M., Zhou, Y.: On the stability of first order impulsive evolution equations. Opuscula Math. 34(3), 639–657 (2014)
    • 44. Wang, J.R., Li, X.: A uniform method to Ulam-Hyers stability for some linear fractional equations. Mediterr. J. Math. 13, 625–635 (2016)
    • 45. Wang, X., Rizwan, R., Lee, J.R., Zada, A., Shah, S.O.: Existence, uniqueness and Ulam’s stabilities for a class of implicit impulsive...
    • 46. Wang, J.R., Zhang, Y.: A class of nonlinear differential equations with fractional integrable impulses. Commun. Nonlinear Sci. Numer....
    • 47. Younus, A., O’Regan, D., Yasmin, N., Mirza, S.: Stability criteria for nonlinear volterra integrodynamic systems. Appl. Math. Inf. Sci....
    • 48. Zada, A., Ali, S., Li, T.: Analysis of a new class of impulsive implicit sequential fractional differential equations. Int. J. Nonlinear...
    • 49. Zada, A., Shah, O., Shah, R.: Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems. Appl. Math. Comput....
    • 50. Zada, A., Pervaiz, B., Subramanian, M., Popa, I.: Finite time stability for nonsingular impulsive first order delay differential systems....
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno