IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v353y2019icp230-242.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301092
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Deng, Zhen-Guo & Zeng, Sheng-Da, 2015. "Lattice fractional diffusion equation in terms of a Riesz–Caputo difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 335-339.
    3. 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.
    4. Ge, Fudong & Kou, Chunhai, 2015. "Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 308-316.
    5. Ntouyas, Sotiris K. & Etemad, Sina, 2015. "On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 235-243.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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).
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad & Shahram Rezapour & Jessada Tariboon, 2022. "Sequential Fractional Hybrid Inclusions: A Theoretical Study via Dhage’s Technique and Special Contractions," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    2. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
    3. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    4. Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Nazim I Mahmudov & Sameer Bawaneh & Areen Al-Khateeb, 2019. "On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    6. Abdelkader Moumen & Abdelaziz Mennouni & Mohamed Bouye, 2023. "A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    7. Nazim I Mahmudov & Areen Al-Khateeb, 2019. "Stability, Existence and Uniqueness of Boundary Value Problems for a Coupled System of Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    8. Zhao, Yulin & Chen, Haibo & Qin, Bin, 2015. "Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 417-427.
    9. Zhao, Yulin & Chen, Haibo & Xu, Chengjie, 2017. "Nontrivial solutions for impulsive fractional differential equations via Morse theory," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 170-179.
    10. 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.
    11. Bashir Ahmad & Ymnah Alruwaily & Ahmed Alsaedi & Sotiris K. Ntouyas, 2019. "Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    12. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
    13. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    14. Jarunee Soontharanon & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    15. Suphawat Asawasamrit & Woraphak Nithiarayaphaks & Sotiris K. Ntouyas & Jessada Tariboon, 2019. "Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    16. Zeng, Shengda & Baleanu, Dumitru & Bai, Yunru & Wu, Guocheng, 2017. "Fractional differential equations of Caputo–Katugampola type and numerical solutions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 549-554.
    17. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad, 2019. "Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
    19. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    20. Abbaszadeh, Mostafa & Dehghan, Mehdi, 2021. "Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error estimation," Applied Mathematics and Computation, Elsevier, vol. 392(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:230-242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.