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Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales

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  • Shah, Syed Omar
  • Zada, Akbar

Abstract

In this paper, we study the existence and uniqueness of solution and stability results of mixed integral dynamic system with instantaneous and noninstantaneous impulses on time scales, by using the fixed point method. The main tools to establish our results are the Grönwall’s inequality on time scales, Picard operator and abstract Grönwall lemma. Some assumptions are made to overcome the hurdles in achieving our results. At the end, an example is given that shows the validity of our main results.

Suggested Citation

  • Shah, Syed Omar & Zada, Akbar, 2019. "Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 202-213.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:202-213
    DOI: 10.1016/j.amc.2019.04.044
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    References listed on IDEAS

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    1. Zada, Akbar & Shah, Omar & Shah, Rahim, 2015. "Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 512-518.
    2. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
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    Cited by:

    1. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    2. Akbar Zada & Shaheen Fatima & Zeeshan Ali & Jiafa Xu & Yujun Cui, 2019. "Stability Results for a Coupled System of Impulsive Fractional Differential Equations," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    3. Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    4. Alam, Mehboob & Shah, Dildar, 2021. "Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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