Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Faculty Publications Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Sherly, K.; Veeresha, Pundikala; Baskonus, Haci Mehmet Title A name given to the resource On the Investigation of Environmental Effects of ChatGPT Usage via the Newly Developed Mathematical Model in Caputo Sense Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2026 Source A related resource from which the described resource is derived Fractal and Fractional;Volume;10;Issue;3;Article No.;184; Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.3390/fractalfract10030184" target="_blank" rel="noreferrer noopener">https://doi.org/10.3390/fractalfract10030184</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105033685850?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105033685850?origin=resultslist</a> Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant 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 Description An account of the resource 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. Subject The topic of the resource artificial intelligence; ChatGPT; CO₂ emission; prophet forecasting model; semi-implicit L1 method Publisher An entity responsible for making the resource available Multidisciplinary Digital Publishing Institute (MDPI) Relation A related resource ISSN: 25043110; Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource All Open Access; Gold Open Access; Green Open Access Format The file format, physical medium, or dimensions of the resource online