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Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Author

Listed:
  • Akbar Zada

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

  • Shaheen Fatima

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

  • Zeeshan Ali

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

  • Jiafa Xu

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China)

  • Yujun Cui

    (State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:927-:d:273807
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    References listed on IDEAS

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    1. 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.
    2. Naveed Ahmad & Zeeshan Ali & Kamal Shah & Akbar Zada & Ghaus ur Rahman, 2018. "Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations," Complexity, Hindawi, vol. 2018, pages 1-15, February.
    3. Zeeshan Ali & Poom Kumam & Kamal Shah & Akbar Zada, 2019. "Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-26, April.
    4. Yujun Cui, 2017. "Multiplicity Results for Positive Solutions to Differential Systems of Singular Coupled Integral Boundary Value Problems," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-7, June.
    5. Usman Riaz & Akbar Zada & Zeeshan Ali & Manzoor Ahmad & Jiafa Xu & Zhengqing Fu, 2019. "Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-20, June.
    6. 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. Rui Kang & Shang Gao, 2022. "Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control," Mathematics, MDPI, vol. 10(18), pages 1-9, September.

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