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Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives

Author

Listed:
  • Usman Riaz
  • Akbar Zada
  • Zeeshan Ali
  • Manzoor Ahmad
  • Jiafa Xu
  • Zhengqing Fu

Abstract

This work is committed to establishing the assumptions essential for at least one and unique solution of a switched coupled system of impulsive fractional differential equations having derivative of Hadamard type. Using Krasnoselskii’s fixed point theorem, the existence, as well as uniqueness results, is obtained. Along with this, different kinds of Hyers–Ulam stability are discussed. For supporting the theory, example is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:5093572
    DOI: 10.1155/2019/5093572
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    Cited by:

    1. 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.
    2. Jiafa Xu & Jiqiang Jiang & Donal O’Regan, 2020. "Positive Solutions for a Class of p -Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(3), pages 1-13, February.
    3. Youzheng Ding & Jiafa Xu & Zhengqing Fu, 2019. "Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities," Mathematics, MDPI, vol. 7(10), pages 1-19, October.
    4. Usman Riaz & Akbar Zada & Zeeshan Ali & Ioan-Lucian Popa & Shahram Rezapour & Sina Etemad, 2021. "On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    5. 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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