IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v206y2023icp286-301.html
   My bibliography  Save this article

Legendre approximation method for computing eigenvalues of fourth order fractional Sturm–Liouville problem

Author

Listed:
  • Aghazadeh, A.
  • Mahmoudi, Y.
  • Saei, F.D.

Abstract

In this paper, a special class of fractional Sturm–Liouville problems of order α (3<α≤4) is discussed. The method is based on utilizing the shifted Legendre polynomials on the interval [0,L] to find numerical approximations for eigenvalues and corresponding eigenfunctions. The proposed method is implemented on several numerical examples. The numerical results indicate the high performance of the method, its effectiveness, and its simplicity in use.

Suggested Citation

  • Aghazadeh, A. & Mahmoudi, Y. & Saei, F.D., 2023. "Legendre approximation method for computing eigenvalues of fourth order fractional Sturm–Liouville problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 286-301.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:286-301
    DOI: 10.1016/j.matcom.2022.11.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004566
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.11.007?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. Syam, Muhammed I. & Siyyam, Hani I., 2009. "An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 659-665.
    2. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    3. Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    4. Zhang, Maozhu & Li, Kun, 2020. "Dependence of eigenvalues of Sturm–Liouville problems with eigenparameter dependent boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    5. Al-Mdallal, Qasem M. & Syam, Muhammed I., 2014. "The Chebyshev collocation-path following method for solving sixth-order Sturm–Liouville problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 391-398.
    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. Goel, Eti & Pandey, Rajesh K. & Yadav, S. & Agrawal, Om P., 2023. "A numerical approximation for generalized fractional Sturm–Liouville problem with application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 417-436.
    2. Ji, Antong & Xu, Meizhen, 2024. "Dependence of eigenvalues for higher odd-order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    3. Muhammed I. Syam & Azza Alsuwaidi & Asia Alneyadi & Safa Al Refai & Sondos Al Khaldi, 2018. "An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem," Mathematics, MDPI, vol. 6(7), pages 1-11, June.
    4. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    5. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    6. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.
    7. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. He, Ying & Zuo, Qian, 2021. "Jacobi-Davidson method for the second order fractional eigenvalue problems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. M. M. Khashshan & Muhammed I. Syam & Ahlam Al Mokhmari, 2018. "A Reliable Method for Solving Fractional Sturm–Liouville Problems," Mathematics, MDPI, vol. 6(10), pages 1-10, September.

    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:matcom:v:206:y:2023:i:c:p:286-301. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.