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Stability in System of Impulsive Neutral Functional Differential Equations

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Abstract

In this paper, we use the fixed point theorem to obtain asymptotic stability of the zero solution of a nonlinear impulsive neutral system of differential equations. The results given in Mesmouli etal. (Dyn. Syst. Appl. 25, 253–262, 2016) and Ibanez (2016) are generalized and improved.

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Notes

  1. Notice that \(\delta _{0}<L\) since \(K\ge 1\) and \(1-\alpha <1\).

References

  1. Burton, T.A., Furumochi, T.: Fixed points and problems in stability theory for ordinary and functional differential equations. Dyn. Syst. Appl. 10, 89–116 (2001)

    MathSciNet  MATH  Google Scholar 

  2. Burton, T.A., Furumochi, T.: A note on stability by Schauder’s theorem. Funkcial. Ekvac. 44, 73–82 (2001)

    MathSciNet  MATH  Google Scholar 

  3. Burton, T.A.: Stability by fixed point theory or Liapunov’s theory: a comparison. Fixed Point Theory 4, 15–32 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Burton, T.A.: Stability by fixed point methods for highly nonlinear delay equations. Fixed Point Theory 5(1), 3–20 (2004)

    MathSciNet  MATH  Google Scholar 

  5. Burton, T.A.: Stability by Fixed Point Theory for Func2tional Differential Equations. Dover Publications, New York (2006)

    Google Scholar 

  6. Hu, C., Jiang, H., Teng, Z.: Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Trans. Neural Networks 21(1), 67–81 (2010)

    Article  Google Scholar 

  7. Mesmouli, M.B., Ardjouni, A., Djoudi, A.: Stability solutions for a system of nonlinear neutral functional differential equations with functional delay. Dyn. Syst. Appl. 25, 253–262 (2016)

    MathSciNet  MATH  Google Scholar 

  8. Ibanez, C. R. Stability of Nonlinear Functional Differential Equations by the Contraction Mapping Principle. UWSpace. (2016) http://hdl.handle.net/10012/10707

  9. Zhang, B.: Contraction mapping and stability in a delay-differential equation. Proc. Dyn. Syst. Appl. 4, 189–190 (2004)

    Google Scholar 

  10. Zhang, B.: Fixed points and stability in differential equations with variable delays. Nonlinear Anal. Theory Methods Appl. 63(5–7), 233–242 (2005)

    Article  Google Scholar 

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Acknowledgements

The author would like to thank the anonymous referees for their valuable remarks and suggestions.

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  1. Mathematics Department, Faculty of Science, University of Ha’il, Ha’il, Kingdom of Saudi Arabia

    Mouataz Billah Mesmouli

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  1. Mouataz Billah Mesmouli
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Correspondence to Mouataz Billah Mesmouli.

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Mesmouli, M.B. Stability in System of Impulsive Neutral Functional Differential Equations. Mediterr. J. Math. 18, 32 (2021). https://doi.org/10.1007/s00009-020-01659-4

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  • DOI: https://doi.org/10.1007/s00009-020-01659-4

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