A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor

Haroon Ahmad; Mohammad Azhar Peerzada; Wardah Wardah

Research Article

A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor

Year 2025, Volume: 1 Issue: 1, 22 - 36, 29.12.2025

Haroon Ahmad , Mohammad Azhar Peerzada , Wardah Wardah

Abstract

In this paper, we study a generalized contraction in a complete metric space using a different approach from classical methods, providing a more flexible framework than Banach, Kannan, or Chatterjea contractions. We present two illustrative examples, one involving a continuous mapping and the other a discontinuous mapping, which satisfy the generalized contraction but fail under classical contraction conditions. As an application, we employ this generalized contraction to establish the existence and uniqueness of solutions for a fractional-order Thomas cyclically symmetric attractor via the Caputo-Fabrizio derivative. The results reveal the complex dynamical behavior and sensitivity to initial conditions, demonstrating the effectiveness of the generalized contraction approach in analyzing nonlinear and chaotic systems.

Keywords

Fixed points , Caputo-Fabrizio , Thomas cyclically symmetric attractor

References

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There are 33 citations in total.

Details

Primary Language	English
Subjects	Operator Algebras and Functional Analysis, Dynamical Systems in Applications
Journal Section	Research Article
Authors	Haroon Ahmad 0000-0002-3907-0554 Mohammad Azhar Peerzada 0000-0002-3907-0555 Wardah Wardah This is me 0009-0005-7529-8432
Submission Date	November 30, 2025
Acceptance Date	December 23, 2025
Early Pub Date	December 29, 2025
Publication Date	December 29, 2025
Published in Issue	Year 2025 Volume: 1 Issue: 1

Cite

APA	Ahmad, H., Peerzada, M. A., & Wardah, W. (2025). A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor. Sakarya Journal of Mathematics, 1(1), 22-36.
AMA	Ahmad H, Peerzada MA, Wardah W. A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor. Sakarya Journal of Mathematics. December 2025;1(1):22-36.
Chicago	Ahmad, Haroon, Mohammad Azhar Peerzada, and Wardah Wardah. “A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor”. Sakarya Journal of Mathematics 1, no. 1 (December 2025): 22-36.
EndNote	Ahmad H, Peerzada MA, Wardah W (December 1, 2025) A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor. Sakarya Journal of Mathematics 1 1 22–36.
IEEE	H. Ahmad, M. A. Peerzada, and W. Wardah, “A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor”, Sakarya Journal of Mathematics, vol. 1, no. 1, pp. 22–36, 2025.
ISNAD	Ahmad, Haroon et al. “A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor”. Sakarya Journal of Mathematics 1/1 (December2025), 22-36.
JAMA	Ahmad H, Peerzada MA, Wardah W. A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor. Sakarya Journal of Mathematics. 2025;1:22–36.
MLA	Ahmad, Haroon et al. “A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor”. Sakarya Journal of Mathematics, vol. 1, no. 1, 2025, pp. 22-36.
Vancouver	Ahmad H, Peerzada MA, Wardah W. A Fixed Point Approach to the Existence and Uniqueness of Solutions for Thomas Cyclically Symmetric Attractor. Sakarya Journal of Mathematics. 2025;1(1):22-36.

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Authors take into account the feedback, criticisms, and recommendations of the reviewer and the Editorial Board. In case of any disagreement, they have the right to appeal with their justifications. Authors edit the article as per the reports and upload the final version of the article to the system.

Field Editor Review

The field editor checks whether the author has made the requested corrections in the text. If there is a “Major Revision” requirement in the peer review reports, they send the article to the relevant peer reviewer. If there is an "Acceptance" or "Minor Revision" requirement and the revisions are completed, they can submit the article for language checks (The checking process is completed within a maximum of 7 days.). If they detect that the corrections have not been made, they re-send the article to the author. They may reject the article if the author does not make the corrections again. Articles that are not accepted for publication are not deleted from the system. Their processes and files are stored in the system.

English Language Checks

Studies are reviewed by the English Language Editor, and if necessary, corrections are requested from the author. The checking process is completed within a maximum of 15 days.

Editorial Board Review

The articles that pass technical, academic, and linguistic reviews are examined by the Editorial Board, and the final publication status is determined. In case of any objection from the members, the Board decides by a majority of votes.

Typesetting and Layout Process

The journal undertakes the typesetting and layout processes of the studies decided to be published by the Editorial Board.

Language

SJM publishes articles written in English.

Change of Authorship

SJM accepts article authors according to the article's title page statement. Therefore, it is the responsibility of the authors to submit the final version of the full author list. Requests for any change of authorship after the submission of the article (e.g., removal/addition of authors, change of order, etc.) are subject to editorial approval. The Editorial Board will investigate such cases and act according to the COPE flowcharts.

Requests for a change of authorship should be conveyed to the Editor with an official letter stating the reasons for the change. The letter should be signed by all the authors and include their confirmation of the change of authorship. If the request is approved by the Editorial Board, the authors are required to submit a new Copyright Agreement Form according to the final author list.

Objections and Appeals

The Editorial Board of the journal deals with objections and appeals within the scope of COPE guidelines. Authors can contact the Editorial Office directly for their objections and appeals. When needed, an impartial representative will be appointed for issues that cannot be resolved by the Editorial Board. The editor-in-chief will make the final decision regarding objections and appeals in the decision-making process.

Disclaimer

The opinions expressed in the articles published in the journal are those of the author(s). They do not purport to reflect the opinions or views of the SJM and its Editor-In-Chief, Editors, Editorial Board, or Publisher. The Editor-in-Chief, Editors, Editorial Board, and Publisher assume no responsibility or liability for such cases. The sole responsibility for the published content lies with the authors.

Price Policy

Sakarya Journal of Mathematics (SJM) does not request fees for article submission, reviewing and editing processes, page layout, or publication (page or color fees).
SJM does not pay any fees to authors, reviewers, editors, and editorial board members.
All papers on SJM are free to read and download.
SJM signed on to the Budapest Open Access Initiative (BOAI), which promotes free access to research literature and has adopted the Open Access Principles clarified in this initiative.
SJM is an open-access journal that does not require any subscription fees.
We do not offer a reprint service for those requiring professional-quality paper reproductions.s
Due to its publication policy, SJM does not accept announcements, advertisements, sponsorships, etc..