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Abstract

In this work,\floatquery[-14pc]AU: Please provide ORCID ID for remaining authors. we study the solvability and stability of the fuzzy reaction-diffusion equation and the fuzzy diffusion equation with nonhomogeneous boundary conditions. Firstly, we derive the fuzzy exact solutions by converting the nonhomogeneous boundary condition to a homogeneous condition, then we prove the instability of the solution by using simulation approach with the help of Maple program. From this, we have decided to implement the fuzzy backstepping approach to developed the stabilization of the fuzzy parabolic partial differential equations. By using this approach together with the generalized Hukuhara (gH) derivative, we were able to find the control solution for the unstable equations and prove the stability of the fuzzy control solutions through simulation.

Reason for Retraction

This article has been retracted at the request of the Editorial Office, following an internal investigation conducted in accordance with the Committee on Publication Ethics (COPE) Retraction Guidelines.

The investigation identified serious concerns affecting the integrity and reliability of the published work. Specifically, one or more of the following issues were confirmed:

  1. Undisclosed use of computer-generated text and/or data, in which substantial portions of the content were produced using algorithmic or artificial intelligence–based tools without transparent disclosure, contrary to the journal's authorship and transparency policies.

  2. Compromised peer-review process, indicating irregularities that undermine the validity, independence or authenticity of the review procedure.

  3. Inappropriate or misleading citations, including references that are irrelevant, improperly used, or appear to artificially inflate citation metrics, thereby distorting the scholarly record.

  4. Authorship-related concerns, including the addition of new author(s) at a later stage of the publication process without adequate justification, documentation, or transparent disclosure, raising unresolved questions regarding author contributions, responsibility, and compliance with the journal's authorship criteria.

The Editorial Office determined that these issues significantly compromise the scientific integrity of the article, and that correction alone would be insufficient to address the concerns. Retraction was therefore deemed necessary to maintain the accuracy and trustworthiness of the scholarly record.

The authors were informed of the findings and the retraction decision. While the authors do not respond to this retraction, the journal has proceeded with the retraction in line with COPE guidance, which permits retraction without author consent when editorial integrity is at risk.

This retraction is issued to alert readers that the findings and conclusions of the article should not be relied upon. The original article will remain accessible for the sake of the scholarly record, but it will be clearly marked as retracted.

Apologies are offered to readers of the journal that this was not detected during the submission process.

Please see the Retraction Notice available at: https://ijcsm.researchcommons.org/ijcsm/vol6/iss4/13

DOI: https://doi.org/10.52866/2788-7421.1365

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