ItemArticle

On the Investigation of Environmental Effects of ChatGPT Usage via the Newly Developed Mathematical Model in Caputo Sense

Title
On the Investigation of Environmental Effects of ChatGPT Usage via the Newly Developed Mathematical Model in Caputo Sense
Creator
Sherly, K.; Veeresha, Pundikala; Baskonus, Haci Mehmet
Description
This study explores the interconnection between the variables of ChatGPT usage, energy consumption, water consumption, and carbon dioxide CO2 emissions. A new integer and fractional order model using the Caputo derivative is proposed to comprehend the long-term dependencies of these variables. Boundedness, and global and local stability are examined for the fractional order model. The equilibrium points of these variables are shown to determine the stability of the model. The RungeKutta 7 numerical method is employed for the integer order model, whereas the semi-implicit linear interpolation (L1) method is used for the fractional order model. The parameter sensitivity is conducted on the systems parameters to understand the variables impact by varying the relevant parameters for the system. To increase the efficacy of our analysis, we used machine learning approaches to model and predict the dynamics of CO2 emissions, energy and water consumption, and ChatGPT usage. The Prophet ML model stood out among the other methods because it is adept at identifying long-term growth trends, seasonal changes, and the impact of outside variables in intricate time-series data. It is extremely beneficial for research centered on sustainability, where accurate projections are essential for wellinformed decision-making, because it can produce robust, interpretable forecasts against missing values and outliers. Using the Prophet ML model, our research guarantees precise and expandable predictions and provides valuable information that can direct tactics to balance environmental sustainability and technological progress. 2026 by the authors.
Source
Fractal and Fractional;Volume;10;Issue;3;Article No.;184;
Date
01-01-2026
Publisher
Multidisciplinary Digital Publishing Institute (MDPI)
Subject
artificial intelligence; ChatGPT; CO2 emission; prophet forecasting model; semi-implicit L1 method
Coverage
Sherly K., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Baskonus H.M., Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, 63190, Turkey
Rights
All Open Access; Gold Open Access; Green Open Access
Relation
ISSN: 25043110;
Format
online
Language
English
Type
Article

Citation

Sherly, K.; Veeresha, Pundikala; Baskonus, Haci Mehmet, “On the Investigation of Environmental Effects of ChatGPT Usage via the Newly Developed Mathematical Model in Caputo Sense,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 19, 2026, https://archives.christuniversity.in/items/show/23528.

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