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Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives

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  • Liu, Xiping
  • Jia, Mei

Abstract

We study the three-point boundary value problems for the fractional differential coupled systems with both left and right fractional derivatives in the paper. Firstly, the upper-lower solutions method for the systems is presented and some existence results to the systems solutions are also obtained. Secondly, we also give out an iterative approach for finding approximate solutions of the systems. Finally, we consider a concrete example where we obtain the existence result of the solution and also give out its numerical solution and the graphical simulation.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:230-242
    DOI: 10.1016/j.amc.2019.02.011
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    References listed on IDEAS

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    1. Han, Zhenlai & Lu, Hongling & Zhang, Chao, 2015. "Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 526-536.
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    4. Jia, Mei & Liu, Xiping, 2014. "Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 313-323.
    5. 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.
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    Cited by:

    1. Hou, Mimi & Xi, Xuan-Xuan & Zhou, Xian-Feng, 2021. "Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    2. Blaszczyk, Tomasz & Siedlecki, Jaroslaw & Sun, HongGuang, 2021. "An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    3. 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).

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