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A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions

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  • Aljoudi, Shorog
  • Ahmad, Bashir
  • Nieto, Juan J.
  • Alsaedi, Ahmed

Abstract

We study a nonlocal boundary value problem of Hadamard type coupled sequential fractional differential equations supplemented with coupled strip conditions (nonlocal Riemann-Liouville integral boundary conditions). The nonlinearities in the coupled system of equations depend on the unknown functions as well as their lower order fractional derivatives. We apply Leray-Schauder alternative and Banach’s contraction mapping principle to obtain the existence and uniqueness results for the given problem. An illustrative example is also discussed.

Suggested Citation

  • Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:39-46
    DOI: 10.1016/j.chaos.2016.05.005
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    References listed on IDEAS

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    1. Yajing Li & Yejuan Wang, 2013. "Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, November.
    2. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    3. Bashir Ahmad & Jorge Losada & Juan J. Nieto, 2015. "On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, June.
    4. Area, Iván & Losada, Jorge & Nieto, Juan J., 2016. "A note on the fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 182-187.
    5. Ma, Qinghua & Wang, Rongnian & Wang, Junwei & Ma, Yicheng, 2015. "Qualitative analysis for solutions of a certain more generalized two-dimensional fractional differential system with Hadamard derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 436-445.
    6. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
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    Cited by:

    1. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
    2. Nemat Nyamoradi & Sotiris K. Ntouyas & Jessada Tariboon, 2022. "Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    3. Pei, Ke & Wang, Guotao & Sun, Yanyan, 2017. "Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 158-168.
    4. Ahmed Alsaedi & Rodica Luca & Bashir Ahmad, 2020. "Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p -Laplacian Operators," Mathematics, MDPI, vol. 8(11), pages 1-18, October.
    5. Jiqiang Jiang & Donal O’Regan & Jiafa Xu & Yujun Cui, 2019. "Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    6. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
    7. Agarwal, Ravi P. & Ahmad, Bashir & Garout, Doa’a & Alsaedi, Ahmed, 2017. "Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 149-161.
    8. 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.
    9. Shahram Rezapour & Salim Ben Chikh & Abdelkader Amara & Sotiris K. Ntouyas & Jessada Tariboon & Sina Etemad, 2021. "Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems," Mathematics, MDPI, vol. 9(7), pages 1-17, March.
    10. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.

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