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Coupled Systems of Nonlinear Integer and Fractional Differential Equations with Multi-Point and Multi-Strip Boundary Conditions

Author

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  • Bin Di

    (College of Science, China Agricultural University, Beijing 100083, China)

  • Guo Chen

    (International College Beijing, China Agricultural University, Beijing 100083, China)

  • Huihui Pang

    (College of Science, China Agricultural University, Beijing 100083, China)

Abstract

We first consider a second order coupled differential system with nonlinearities involved two unknown functions and their derivatives, subject to a new kinds of multi-point and multi-strip boundary value conditions. Since the coupled system contains two dependent variables and their derivatives, the classical method of upper and lower solutions on longer applies. So we adjust and redefine the forms of upper and lower solutions, to establish the existence results. Secondly, we study a Caputo fractional order coupled differential system with discrete multi-point and integral multi-strip boundary value conditions which are very popular recently, and can accurately describe a lot of practical dynamical phenomena, such as control theory, biological system, electroanalytical chemistry and so on. In this part the existence and uniqueness results are achieved via the Leray-Schauder’s alternative and the Banach’s contraction principle. Finally, an example is presented to illustrate the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:935-:d:368567
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    References listed on IDEAS

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    1. 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.
    2. Wenzhe Xie & Jing Xiao & Zhiguo Luo, 2014. "Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    3. 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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