IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v186y2024ics0960077924008658.html
   My bibliography  Save this article

A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations

Author

Listed:
  • Savadkoohi, Fateme Rezaei
  • Rabbani, Mohsen
  • Allahviranloo, Tofigh
  • Malkhalifeh, Mohsen Rostamy

Abstract

In this article, we construct a fractional multi-wavelet basis based on Legendre polynomials to solve fractional delay linear and nonlinear differential equations. For this we introduce an orthonormal fractional basis for Banach space L2[0,1] with suitable inner product which make it effective to decrease computational operations and increase accuracy to find approximate solution of the equations. Also, solving fractional problems by orthogonal basis such as Legendre polynomials has a lower accuracy in comparison with fractional basis. Finally, some examples are solved to show the high accuracy of the presented method, and also to compare with some other works.

Suggested Citation

  • Savadkoohi, Fateme Rezaei & Rabbani, Mohsen & Allahviranloo, Tofigh & Malkhalifeh, Mohsen Rostamy, 2024. "A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008658
    DOI: 10.1016/j.chaos.2024.115313
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924008658
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115313?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. Devi, Vinita & Maurya, Rahul Kumar & Singh, Somveer & Singh, Vineet Kumar, 2020. "Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Syam, Muhammed I. & Sharadga, Mwaffag & Hashim, I., 2021. "A numerical method for solving fractional delay differential equations based on the operational matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Pensri Pramukkul & Adam Svenkeson & Paolo Grigolini & Mauro Bologna & Bruce West, 2013. "Complexity and the Fractional Calculus," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-7, April.
    4. Maurya, Rahul Kumar & Li, Dongxia & Singh, Anant Pratap & Singh, Vineet Kumar, 2024. "Numerical algorithm for a general fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 405-432.
    5. Saeed, Umer & Rehman, Mujeeb ur & Iqbal, Muhammad Asad, 2015. "Modified Chebyshev wavelet methods for fractional delay-type equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 431-442.
    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. Usman, M. & Hamid, M. & Zubair, T. & Haq, R.U. & Wang, W. & Liu, M.B., 2020. "Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    3. Sondos M. Syam & Z. Siri & Sami H. Altoum & R. Md. Kasmani, 2023. "An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science," Mathematics, MDPI, vol. 11(14), pages 1-21, July.
    4. Usman, Muhammad & Hamid, Muhammad & Khan, Zafar Hayat & Haq, Rizwan Ul, 2021. "Neuronal dynamics and electrophysiology fractional model: A modified wavelet approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    5. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Chen, Zhong & Gou, QianQian, 2019. "Piecewise Picard iteration method for solving nonlinear fractional differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 465-478.
    7. Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-26, May.
    8. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    9. Grigolini, Paolo, 2015. "Emergence of biological complexity: Criticality, renewal and memory," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 575-588.
    10. Zare, Marzieh & Grigolini, Paolo, 2013. "Criticality and avalanches in neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 80-94.
    11. Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(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:chsofr:v:186:y:2024:i:c:s0960077924008658. 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.