IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v128y2019icp366-381.html
   My bibliography  Save this article

Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus

Author

Listed:
  • Atangana, Abdon
  • Mekkaoui, Toufik

Abstract

Human being live in three-dimensional space; they can accurately visualize processes taking place in one, two and three dimensions. Although the set of bi-complex numbers and quaternion have attracted attention of many researchers in physics and related branches, they do not really represent processes taking place in the space where human being are located. We suggested a new set of complex number called “the Trinition”. The new set is comprised between complex number with one imaginary part and complex number with three imaginary parts called quaternion/bi-complex numbers. We established a bijection between the new set and the three-dimensional space. We presented some important properties of the new set. We showed that all chaotic attractors in three dimension are simply three-dimensional mapping in the new set. Fewer examples of mapping in such set were presented. A new methodology that can be used to obtain more strange attractors are equally suggested. The methodology combines fractional chaotic models and some fractal mapping within the new set. Some illustrative figures are presented.

Suggested Citation

  • Atangana, Abdon & Mekkaoui, Toufik, 2019. "Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 366-381.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:366-381
    DOI: 10.1016/j.chaos.2019.08.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919303285
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.08.018?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Mehmet Yavuz & Ndolane Sene & Mustafa Yıldız, 2022. "Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    5. Sene, Ndolane, 2020. "Second-grade fluid model with Caputo–Liouville generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Mohamed, Sara M. & Sayed, Wafaa S. & Said, Lobna A. & Radwan, Ahmed G., 2022. "FPGA realization of fractals based on a new generalized complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

    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:128:y:2019:i:c:p:366-381. 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.