IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2025y2025i1n8384630.html

Fractals and Chaotic Solitons Phenomena in Conformable Coupled Higgs System

Author

Listed:
  • Naveed Iqbal
  • Wael W. Mohammed
  • Amjad E. Hamza
  • Shah Hussain
  • Yousef Jawarneh
  • Rasool Shah

Abstract

The current study aims to construct and examine a new plethora of soliton solutions for the conformable coupled Higgs system (CCHS), a system of nonlinear fractional partial differential equations (NFPDEs) which was initially presented utilize a systematic structure to consider the responsive mechanism of the Higgs system in the electroweak theory perspective, within the framework of the standard model of physics. To achieve our goal, we utilize a transformation‐based analytical technique, namely, the generalized Bernoulli equation method (gBEM), which reduces CCHS to nonlinear ordinary differential equations (NODEs) via a fractional complex transformation. The fresh assortment of soliton solutions is produced when the resultant NODEs are tackled using the Maple tool. We employ 3D and contour visualizations to graphically represent the behavior of acquired solitons, which prominently reveal that these soliton solutions show axial, chaotic, and periodic perturbations which induce instabilities in soliton and may lead to the formation of fractals. The results appear groundbreaking, showcasing diverse families of soliton solutions with intricate interrelations and dynamics. These findings not only advance our theoretical understanding of CCHS dynamics but they may also have implications in NFPDE–related fields.

Suggested Citation

  • Naveed Iqbal & Wael W. Mohammed & Amjad E. Hamza & Shah Hussain & Yousef Jawarneh & Rasool Shah, 2025. "Fractals and Chaotic Solitons Phenomena in Conformable Coupled Higgs System," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:8384630
    DOI: 10.1155/ddns/8384630
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ddns/8384630
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ddns/8384630?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. Ma’mon Abu Hammad, 2021. "Conformable Fractional Martingales and Some Convergence Theorems," Mathematics, MDPI, vol. 10(1), pages 1-4, December.
    2. Brajesh Kumar Singh & Pramod Kumar, 2017. "Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-11, March.
    3. Hassan Khan & Rasool Shah & Poom Kumam & Dumitru Baleanu & Muhammad Arif, 2019. "An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    4. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    5. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland, 2022. "Analysis of the Fuzzy Fractional‐Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo‐Fabrizio Derivative," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    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. Nagwa A. Saeed & Deepak B. Pachpatte, 2025. "An Approach to Solve Fuzzy Fractional Darboux Problems Under the Caputo Derivative," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    2. Abiodun Ezekiel Owoyemi & Chang Phang & Yoke Teng Toh, 2022. "An Efficient Numerical Scheme for Solving Multiorder Tempered Fractional Differential Equations via Operational Matrix," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    3. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    4. Yong Tang, 2023. "Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model," Mathematics, MDPI, vol. 11(11), pages 1-12, June.
    5. 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.
    6. Khudhayr A. Rashedi & Musawa Yahya Almusawa & Hassan Almusawa & Tariq S. Alshammari & Adel Almarashi, 2025. "Fractional Dynamics: Applications of the Caputo Operator in Solving the Sawada–Kotera and Rosenau–Hyman Equations," Mathematics, MDPI, vol. 13(2), pages 1-23, January.
    7. Abdellatif Ben Makhlouf & Lassaad Mchiri & Hakeem A. Othman & Hafedh M. S. Rguigui & Salah Boulaaras, 2023. "Proportional Itô–Doob Stochastic Fractional Order Systems," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    8. Wedad Albalawi & Rasool Shah & Nehad Ali Shah & Jae Dong Chung & Sherif M. E. Ismaeel & Samir A. El-Tantawy, 2023. "Analyzing Both Fractional Porous Media and Heat Transfer Equations via Some Novel Techniques," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    9. Alberto Antonini & Valentina Anna Lia Salomoni, 2023. "Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition," Mathematics, MDPI, vol. 11(12), pages 1-30, June.
    10. Khudhayr A. Rashedi & Musawa Yahya Almusawa & Hassan Almusawa & Tariq S. Alshammari & Adel Almarashi, 2024. "Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences," Mathematics, MDPI, vol. 13(1), pages 1-17, December.

    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:wly:jnddns:v:2025:y:2025:i:1:n:8384630. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    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.