IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v378y2020ics009630032030120x.html
   My bibliography  Save this article

Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions

Author

Listed:
  • Jiang, Wei
  • Chen, Zhong
  • Hu, Ning
  • Song, Haiyang
  • Yang, Zhaohong

Abstract

In this paper, we investigate the multi-scale orthogonal basis method for fractional integral boundary value problems. We apply the Newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi-scale orthogonal basis, then the approximation solution is obtained. The error estimation and stable analysis are presented in detailed. The final numerical experiments verify that the accuracy of our method.

Suggested Citation

  • Jiang, Wei & Chen, Zhong & Hu, Ning & Song, Haiyang & Yang, Zhaohong, 2020. "Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s009630032030120x
    DOI: 10.1016/j.amc.2020.125151
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032030120X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125151?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. Tofighi, Ali, 2003. "The intrinsic damping of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 29-34.
    2. Grudziński, Krzysztof & Żebrowski, Jan J, 2004. "Modeling cardiac pacemakers with relaxation oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 153-162.
    Full references (including those not matched with items on IDEAS)

    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. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    3. Tian, Yan & Zhong, Lin-Feng & He, Gui-Tian & Yu, Tao & Luo, Mao-Kang & Stanley, H. Eugene, 2018. "The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 845-856.
    4. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    5. Templos-Hernández, Diana J. & Quezada-Téllez, Luis A. & González-Hernández, Brian M. & Rojas-Vite, Gerardo & Pineda-Sánchez, José E. & Fernández-Anaya, Guillermo & Rodriguez-Torres, Erika E., 2021. "A fractional-order approach to cardiac rhythm analysis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Drozdov, A.D., 2007. "Fractional oscillator driven by a Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 237-245.
    7. Liu, Q.X. & Liu, J.K. & Chen, Y.M., 2017. "An analytical criterion for jump phenomena in fractional Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 216-219.
    8. Fouego, Dorota Youmbi & Dongmo, Eric Donald & Woafo, Paul, 2021. "Voltages responses and synchronization of an array of Grudzinski and Zebrowski oscillators coupled to an electrical load," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Weiwei Liu & Lishan Liu, 2021. "Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives," Mathematics, MDPI, vol. 9(23), pages 1-23, November.
    11. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
    12. Isao Shoji & Masahiro Nozawa, 2020. "A geometric analysis of nonlinear dynamics and its application to financial time series," Papers 2012.11825, arXiv.org.
    13. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    14. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    15. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
    16. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    17. Asher Yahalom & Natalia Puzanov, 2024. "Feedback Stabilization Applied to Heart Rhythm Dynamics Using an Integro-Differential Method," Mathematics, MDPI, vol. 12(1), pages 1-14, January.
    18. Arthi, G. & Park, Ju H. & Suganya, K., 2019. "Controllability of fractional order damped dynamical systems with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 74-91.
    19. Vishwamittar, & Batra, Priyanka & Chopra, Ribhu, 2021. "Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(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:378:y:2020:i:c:s009630032030120x. 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.