IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0305259.html
   My bibliography  Save this article

Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set

Author

Listed:
  • Hind Sweis
  • Omar Abu Arqub
  • Nabil Shawagfeh

Abstract

Fractional calculus serves as a versatile and potent tool for the modeling and control of intricate systems. This discussion debates the system of DFDEs with two regimes; theoretically and numerically. For theoretical analysis, we have established the EUE by leveraging the definition of Hilfer (α,β)-framework. Our investigation involved the examination of the possessions of the FRD, FCD, and FHD, utilizing their forcefulness and qualifications to convert the concerning delay system into an equivalent one of fractional DVIEs. By employing the CMT, we have successfully demonstrated the prescribed requirements. For numerical analysis, the Galerkin algorithm was implemented by leveraging OSLPs as a base function. This algorithm allows us to estimate the solution to the concerning system by transforming it into a series of algebraic equations. By employing the software MATHEMATICA 11, we have effortlessly demonstrated the requirements estimation of the nodal values. One of the key advantages of the deployed algorithm is its ability to achieve accurate results with fewer iterations compared to alternative methods. To validate the effectiveness and precision of our analysis, we conducted a comprehensive evaluation through various linear and nonlinear numerical applications. The results of these tests, accompanied by figures and tables, further support the superiority of our algorithm. Finally, an analysis of the numerical algorithm employed was provided along with insightful suggestions for potential future research directions.

Suggested Citation

  • Hind Sweis & Omar Abu Arqub & Nabil Shawagfeh, 2024. "Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set," PLOS ONE, Public Library of Science, vol. 19(6), pages 1-23, June.
  • Handle: RePEc:plo:pone00:0305259
    DOI: 10.1371/journal.pone.0305259
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0305259
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0305259&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0305259?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
    ---><---

    References listed on IDEAS

    as
    1. Mehmet Zeki Sarikaya & Hasan Ogunmez, 2012. "On New Inequalities via Riemann‐Liouville Fractional Integration," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. ur Rahman, Ghaus & Agarwal, Ravi P. & Ahmad, Dildar, 2022. "Existence and stability analysis of nth order multi term fractional delay differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. 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).
    4. Hind Sweis & Omar Abu Arqub & Nabil Shawagfeh, 2023. "Fractional delay integrodifferential equations of nonsingular kernels: Existence, uniqueness, and numerical solutions using Galerkin algorithm based on shifted Legendre polynomials," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-23, April.
    5. Mehmet Zeki Sarikaya & Hasan Ogunmez, 2012. "On New Inequalities via Riemann-Liouville Fractional Integration," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, October.
    6. 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).
    7. Amin, Rohul & Shah, Kamal & Asif, Muhammad & Khan, Imran, 2021. "A computational algorithm for the numerical solution of fractional order delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    8. F. A. Rihan & C. Tunc & S. H. Saker & S. Lakshmanan & R. Rakkiyappan, 2018. "Applications of Delay Differential Equations in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-3, September.
    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. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2024. "Ulam Stability for Boundary Value Problems of Differential Equations—Main Misunderstandings and How to Avoid Them," Mathematics, MDPI, vol. 12(11), pages 1-22, May.
    2. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. 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).
    4. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. 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.
    6. Hasib Khan & Jehad Alzabut & Haseena Gulzar & Osman Tunç & Sandra Pinelas, 2023. "On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    7. Andrea Aglić Aljinović, 2014. "Montgomery Identity and Ostrowski Type Inequalities for Riemann-Liouville Fractional Integral," Journal of Mathematics, Hindawi, vol. 2014, pages 1-6, September.
    8. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    9. 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).
    10. Yuanheng Wang & Barrira Jurrat & Muddasir Ejaz & Muhammad Azeem & M I Elashiry, 2024. "Existence and uniqueness of well-posed fractional boundary value problem," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-26, May.
    11. Haifa Bin Jebreen & Ioannis Dassios, 2024. "The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations," Mathematics, MDPI, vol. 12(21), pages 1-15, October.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0305259. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.