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Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Author

Listed:
  • Huizhen Qu

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

  • Jianwen Zhou

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

  • Tianwei Zhang

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

Abstract

This paper discusses a kind of coupled nonlocal Laplacian evolution equation with Caputo time-fractional derivatives and proportional delays. Green function and mild solution are firstly established by employing the approach of eigenvalues’ expansions and Fourier analysis technique. By the properties of eigenvalues and Mittag–Leffler functions, several vital estimations of Green functions are presented. In view of these estimations and some appropriate assumptions, the existence and uniqueness of the mild solution are studied by utilizing the Leray–Schauder fixed-point theorem and the Banach fixed-point theorem. Finally, an example is provided to illustrate the effectiveness of our main results.

Suggested Citation

  • Huizhen Qu & Jianwen Zhou & Tianwei Zhang, 2022. "Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2204-:d:846812
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    References listed on IDEAS

    as
    1. Chen Chen & Qixiang Dong, 2022. "Existence and Hyers–Ulam Stability for a Multi-Term Fractional Differential Equation with Infinite Delay," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    2. Hu, Ye & Li, Changpin & Li, Hefeng, 2017. "The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 319-326.
    3. Zhang, Tianwei & Li, Yongkun, 2022. "S-asymptotically periodic fractional functional differential equations with off-diagonal matrix Mittag-Leffler function kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 331-347.
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