Exploring ocean pH dynamics via a mathematical modeling with the Caputo fractional derivative

Global warming is a complex problem with far-reaching global implications. One of its notable repercussions is the escalation of CO₂ C O 2 levels in the atmosphere, resulting in the phenomenon known as Ocean Acidification (OA). In this research, we have established a correlation between four key factors: marine species, human population, CO₂ C O 2 levels, and ocean pH. By formulating a Caputo fractional differential equation, we investigated the dynamics of these variables to evaluate the significance of this climatic phenomenon. The model analysis reveals that the rise in anthropogenic CO₂ C O 2 emissions causes a reduction in the ocean’s pH level and increases OA. This process, in turn, decreases the ocean’s ability to absorb CO₂ C O 2 , making it less effective in mitigating climate change. In this study, it was demonstrated that elevated levels of CO₂ C O 2 result in a reduction in pH levels, which in turn causes a decrease in the population of marine species that play a critical role in numerous economic sectors such as tourism, aquaculture, and fisheries. Moreover, we conducted a comprehensive analysis of the influence exerted by the intrinsic growth rate of the human population. We examined various theoretical aspects, including the assessment of existence and uniqueness. Numerical simulations are carried out to illustrate the effect of key parameters on the dynamics of the system using the generalized Adams–Bashforth–Moulton method.