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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p‐Laplacian Operators

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  • Chen Yang
  • Xiaolin Zhu

Abstract

This paper considers a system of fractional differential equations involving p‐Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=001, 1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈01,,bi∈0,ηi1−αi/pi−1, i = 1, 2, and f, g ∈ C([0, 1] × [0, +∞) × [0, +∞), [0, +∞)) and λ and μ are two positive parameters. We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result.

Suggested Citation

  • Chen Yang & Xiaolin Zhu, 2020. "Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p‐Laplacian Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:9563791
    DOI: 10.1155/2020/9563791
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    References listed on IDEAS

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    1. Haiyan Zhang & Yaohong Li & Jiafa Xu, 2019. "Positive Solutions for a System of Fractional Integral Boundary Value Problems Involving Hadamard-Type Fractional Derivatives," Complexity, Hindawi, vol. 2019, pages 1-11, October.
    2. Moustafa El-Shahed & Wafa M. Shammakh, 2011. "Existence of Positive Solutions for m‐Point Boundary Value Problem for Nonlinear Fractional Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. 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.
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