Fixed point-based stability analysis of climate and Langevin models

PLOS ONE OPEN ACCESS Citation: Shah SK, Ahmed WE, Alabdi I, Alahmade A, Aldwoah K, Hassan EI (2025) Fixed point-based stability analysis of climate and Langevin models. PLoS One 20(7): e0327488. https://doi.org/10.1371/journal.pone.0327488 Editor: Pradip Debnath, Tezpur University, INDIA Received: April 16, 2025 Accepted: June 16, 2025 Published: July 3, 2025 Copyright: © 2025 Shah et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data availability statement: This study is purely theoretical and does not involve any empirical, observational, or simulated data. Therefore, no datasets were generated or analyzed during the current study. Funding: The author(s) received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist. RESEARCH ARTICLE Fixed point-based stability analysis of climate and Langevin models Syed Khayyam Shah1, Waleed Eltayeb Ahmed 2, Ishraq Alabdi 3∗, Ayman Alahmade4, Khaled Aldwoah 5∗, Eltigani I. Hassan2 1 Department of Sustainable Environment and Energy Systems (SEES), Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey, 2 Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia, 3 Department of Mathematics, Hajjah University, Hajjah, Yemen, 4 Department of Mathematics, College of Science, Taibah

University, Medina, Saudi Arabia, 5 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia ∗ iqalabdi@gmail.com (IA) ; aldwoah@iu.edu.sa (KA) Abstract In this manuscript, the existence and uniqueness of solutions to equations associated with climate change are discussed. For this purpose, we utilize some results from the existing literature to investigate the behavior of these equations. Additionally, the role of fixed point theory in emphasizing the importance of proving the stability and consistency of the models is explored. Several definitions and results, such as the F -contraction, 𝛼-F -contraction, rational type ˆ𝜓, 𝜙-contraction, and Geraghty type contraction, are recalled from the existing literature to illustrate their theoretical foundations and practical applications. 1 Introduction Mathematics serves as a highly efficient and potent tool for understanding the world and addressing intricate challenges across diverse scientific fields, engineering, and technology [1–3]. In this context, the crucial role of mathematics cannot be overstated in addressing planetary issues, particularly the connection between society and nature [4,5]. Humans engage in various activities through interactions with their environment. Humans influence the environment by altering its properties, while environmental conditions, in turn, impact human health and survival capabilities. The present climate change, in contrast to other instances, is anthropogenic and marked by an unparalleled acceleration in the global mean

surface temperature (GMST) [6,7]. In [8], it is indicated that from 1880, the GMST has risen upto 0.07 C by an average per decade. In the 21st century, notably in the first two decades, the growth rate of the GMST was 0.17 C for a decade, which is more than twice the average rate. A notable indicator of human activities is the considerable rise in atmospheric carbon diox- ide (CO2) concentrations. This greenhouse gas, a by-product of the combustion of fuels, turns out to be the primary culprit for global warming. This greenhouse gas, a by-product of fuel combustion, is considered the primary driver of global warming. Global warming has impacted climate across nearly all regions of our planet; however, the extent of this effect varies considerably by region [6,7]. Global and regional climate changes PLOS One https://doi.org/10.1371/journal.pone.0327488 July 3, 2025 1/ 18