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A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis

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  • Wang, Fang
  • Liu, Lishan
  • Wu, Yonghong

Abstract

In the paper, we establish the uniqueness of positive solutions for a model of higher-order singular fractional boundary value problems with p-Laplacian operator. The equation includes the Caputo and the Riemann-Liouville fractional derivative. The boundary conditions contain Riemann-Stieltjes integrals and nonlocal infinite-point boundary conditions. The nonlinear terms f and h may be singular on the time variable and space variables. The uniqueness result is obtained, by the theory of mixed monotone operators. We also discuss the dependence of solutions upon a parameter. Furthermore, two examples illustrate our main results via numerical analysis.

Suggested Citation

  • Wang, Fang & Liu, Lishan & Wu, Yonghong, 2020. "A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303052
    DOI: 10.1016/j.amc.2020.125339
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    References listed on IDEAS

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    1. Henderson, Johnny & Luca, Rodica, 2017. "Systems of Riemann–Liouville fractional equations with multi-point boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 303-323.
    2. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
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    Cited by:

    1. 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.
    2. Jong, KumSong & Choi, HuiChol & Kim, MunChol & Kim, KwangHyok & Jo, SinHyok & Ri, Ok, 2021. "On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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