IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i2d10.1007_s10957-025-02643-2.html
   My bibliography  Save this article

Implementation of an Optimization Algorithm for a New General Class of Two-Dimensional Fractional PDEs

Author

Listed:
  • Zakieh Avazzadeh

    (Stony Brook Institute at Anhui University, Anhui University
    University of South Africa)

  • Hossein Hassani

    (Anand International College of Engineering)

  • Mohammad Javad Ebadi

    (Chabahar Maritime University)

  • Ali Bayati Eshkaftaki

    (Shahrekord University)

  • Ahmed Hendy

    (Benha University)

Abstract

In recent years, the inherent numerical difficulties in the study of two-dimensional fractional differential equations (T-FDEs) make them challenging for investigation. In the present contribution, we introduce a new general class of T-FDEs to be solved. Their solution is addressed by the use of unique polynomials of the generalized shifted Legendre functions. For this purpose, we evaluate the association of new fractional and ordinary operational matrices using the Lagrange multipliers algorithm. The analysis of the convergence is done and the existence of a unique solution for the T-FDEs is proved. Three problems are considered to test the proposed methodology. It is pointed out that our methodology can be considered as a promising strategy to solve two-dimensional variable-order fractional differential equations and 2D variable-order fractional optimal control problems.

Suggested Citation

  • Zakieh Avazzadeh & Hossein Hassani & Mohammad Javad Ebadi & Ali Bayati Eshkaftaki & Ahmed Hendy, 2025. "Implementation of an Optimization Algorithm for a New General Class of Two-Dimensional Fractional PDEs," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-22, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02643-2
    DOI: 10.1007/s10957-025-02643-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02643-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-025-02643-2?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. Hesameddini, Esmail & Shahbazi, Mehdi, 2018. "Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 40-54.
    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. Tahereh Eftekhari & Jalil Rashidinia, 2023. "An Investigation on Existence, Uniqueness, and Approximate Solutions for Two-Dimensional Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 11(4), pages 1-29, February.

    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:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02643-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.