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Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions

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  • Agarwal, Ravi P.
  • Ahmad, Bashir
  • Garout, Doa’a
  • Alsaedi, Ahmed

Abstract

We introduce a new concept of coupled flux conditions and unify it with nonlocal coupled strip and multi-point boundary conditions. Equipped with the unified boundary conditions, a nonlinear coupled system of Liouville-Caputo type fractional differential equations is studied. Existence and uniqueness results for the given boundary value problem are obtained by applying Banach’s fixed point theorem and Leray–Schauder alternative, and are well illustrated with the aid of examples. Our work is not only new in the given configuration but also yields several new results as its special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:149-161
    DOI: 10.1016/j.chaos.2017.03.025
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    References listed on IDEAS

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    1. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    2. Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
    3. 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.
    4. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
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    Cited by:

    1. Bin Di & Guo Chen & Huihui Pang, 2020. "Coupled Systems of Nonlinear Integer and Fractional Differential Equations with Multi-Point and Multi-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    2. Suphawat Asawasamrit & Woraphak Nithiarayaphaks & Sotiris K. Ntouyas & Jessada Tariboon, 2019. "Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    3. Weiwei Liu & Lishan Liu, 2021. "Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives," Mathematics, MDPI, vol. 9(23), pages 1-23, November.
    4. Muthaiah Subramanian & Jehad Alzabut & Mohamed I. Abbas & Chatthai Thaiprayoon & Weerawat Sudsutad, 2022. "Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and," Mathematics, MDPI, vol. 10(11), pages 1-19, May.

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