IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v191y2025ics0960077924014048.html
   My bibliography  Save this article

Generalized separable solutions for (2+1) and (3+1)-dimensional m-component coupled nonlinear systems of PDEs under three different time-fractional derivatives

Author

Listed:
  • Prakash, P.
  • Priyendhu, K.S.
  • Lakshmanan, M.

Abstract

In this article, we explain the invariant subspace approach for (2+1) and (3+1)-dimensional m-component nonlinear coupled systems of PDEs with and without time delays under three different time-fractional derivatives. Also, we explain how this method can be used to derive different types of generalized separable solutions for the nonlinear systems mentioned above through the obtained invariant subspaces. More precisely, we show the applicability of this method using the general class of coupled 2-component nonlinear (2+1)-dimensional reaction-diffusion system under three time-fractional derivatives. Moreover, we provide a detailed description for obtaining the various types of different dimensional invariant linear 2-component subspaces and their solutions for the underlying coupled 2-component nonlinear (2+1)-dimensional reaction-diffusion system with appropriate initial-boundary conditions under the three time-fractional derivatives known as (a) Riemann–Liouville (RL) fractional derivative, (b) Caputo fractional derivative, and (c) Hilfer fractional derivative, as examples. Furthermore, we observe that the derived separable solutions under three fractional-order derivatives consist of trigonometric, polynomial, exponential, and Mittag–Leffler functions. Additionally, we present a comparative study of the obtained solutions and results of the discussed nonlinear systems under the three considered fractional derivatives through the corresponding two and three-dimensional plots for various values of fractional orders as well as with the existing literature.

Suggested Citation

  • Prakash, P. & Priyendhu, K.S. & Lakshmanan, M., 2025. "Generalized separable solutions for (2+1) and (3+1)-dimensional m-component coupled nonlinear systems of PDEs under three different time-fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
  • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014048
    DOI: 10.1016/j.chaos.2024.115852
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924014048
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.115852?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.

    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:191:y:2025:i:c:s0960077924014048. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.