IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v181y2024ics0960077924001863.html
   My bibliography  Save this article

Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach

Author

Listed:
  • Ayazi, N.
  • Mokhtary, P.
  • Moghaddam, B. Parsa

Abstract

This paper presents a new approach for solving fractional delay differential equations of variable order using the spectral element method. The proposed method overcomes the limitations of traditional spectral methods, such as poor approximation in long intervals and inefficiency in high degrees. By introducing a variable order differentiation matrix and using basic Lagrangian functions to approximate the solution in each element, the method achieves high accuracy and efficiency. A penalty method is also applied to minimize the jump of fluxes at interface points, and the effectiveness of this approach is analyzed. Finally, three benchmark problems are solved, and the convergence analysis demonstrates the effectiveness and efficiency of the proposed method. In essence, this paper offers a significant contribution to the literature on fractional differential equations and their numerical solution methodologies.

Suggested Citation

  • Ayazi, N. & Mokhtary, P. & Moghaddam, B. Parsa, 2024. "Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001863
    DOI: 10.1016/j.chaos.2024.114635
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924001863
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114635?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. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
    2. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    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. Afshin Babaei & Sedigheh Banihashemi & Behrouz Parsa Moghaddam & Arman Dabiri & Alexandra Galhano, 2024. "Efficient Solutions for Stochastic Fractional Differential Equations with a Neutral Delay Using Jacobi Poly-Fractonomials," Mathematics, MDPI, vol. 12(20), pages 1-20, October.

    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. Baghani, Omid, 2022. "SCW-iterative-computational method for solving a wide class of nonlinear fractional optimal control problems with Caputo derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 540-558.
    2. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
    3. Heydari, Mohammad Hossein & Avazzadeh, Zakieh, 2018. "Legendre wavelets optimization method for variable-order fractional Poisson equation," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 180-190.
    4. Heydari, Mohammad Hossein & Avazzadeh, Zakieh & Haromi, Malih Farzi, 2019. "A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 215-228.
    5. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.
    6. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    7. Araz Noori Dalawi & Mehrdad Lakestani & Elmira Ashpazzadeh, 2022. "An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    8. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    9. Hassani, Hossein & Avazzadeh, Zakieh, 2019. "Transcendental Bernstein series for solving nonlinear variable order fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    10. Fakhrodin Mohammadi & Hossein Hassani, 2019. "Numerical Solution of Two-Dimensional Variable-Order Fractional Optimal Control Problem by Generalized Polynomial Basis," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 536-555, February.
    11. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
    12. Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    13. Habibirad, Ali & Azin, Hadis & Hesameddini, Esmail, 2023. "A capable numerical meshless scheme for solving distributed order time-fractional reaction–diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    14. Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Baghani, Omid, 2021. "Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 343-361.

    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:chsofr:v:181:y:2024:i:c:s0960077924001863. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.