Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey

Mehmet Kocabıyık

doi:10.47000/tjmcs.1589270

Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey

Abstract

The Grey model is a powerful tool for forecasting and modeling systems with incomplete or uncertain data. Its ability to generate accurate predictions with minimal data makes it particularly useful in various fields, including environmental studies. This study enhances the effectiveness of the Grey and Discrete Grey models by incorporating the Hausdorff fractal derivative. The model is applied to real-world data on air pollution, focusing on respirable particulate matter and carbon dioxide emissions. The data, obtained from recent references, have been carefully analysed and used to generate predictions. The predicted values are presented in tabular form, and the impact of applying the Hausdorff fractal derivative on the prediction accuracy under different conditions is demonstrated. The analysis of the data underlines the need for proactive measures to deal with air pollution in the future and highlights the importance of timely intervention to mitigate its adverse effects.

Keywords

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Details

Primary Language

English

Subjects

Numerical Computation and Mathematical Software, Numerical Analysis, Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Mehmet Kocabıyık ^*
0000-0002-7701-6946
Türkiye

Publication Date

February 23, 2026

Submission Date

November 21, 2024

Acceptance Date

November 12, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1589270

IZ

https://izlik.org/JA85WA22KK

Cite

RIS / Bibtex

APA

Kocabıyık, M. (2026). Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey. Turkish Journal of Mathematics and Computer Science, 18(1), 53-66. https://doi.org/10.47000/tjmcs.1589270

AMA

1.Kocabıyık M. Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey. TJMCS. 2026;18(1):53-66. doi:10.47000/tjmcs.1589270

Chicago

Kocabıyık, Mehmet. 2026. “Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey”. Turkish Journal of Mathematics and Computer Science 18 (1): 53-66. https://doi.org/10.47000/tjmcs.1589270.

EndNote

Kocabıyık M (February 1, 2026) Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey. Turkish Journal of Mathematics and Computer Science 18 1 53–66.

IEEE

[1]M. Kocabıyık, “Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey”, TJMCS, vol. 18, no. 1, pp. 53–66, Feb. 2026, doi: 10.47000/tjmcs.1589270.

ISNAD

Kocabıyık, Mehmet. “Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 53-66. https://doi.org/10.47000/tjmcs.1589270.

JAMA

1.Kocabıyık M. Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey. TJMCS. 2026;18:53–66.

MLA

Kocabıyık, Mehmet. “Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 53-66, doi:10.47000/tjmcs.1589270.

Vancouver

1.Mehmet Kocabıyık. Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey. TJMCS. 2026 Feb. 1;18(1):53-66. doi:10.47000/tjmcs.1589270