Analyzing predator-prey dynamics in the context of global warming using fractional integro differential equations

In the field of ecology, the primary focus is on how climate change induced environmental shifts, including increasing temperatures, influence the relationships between species. This study presents a model that we have created to simulate the interactions between two species; one being a predator and the other its prey. In the context of the current situation, we propose using a fractional integro differential model, in line with Caputo's method. The existence of solutions is confirmed, and their stability is analyzed and the existence of unique solution is demonstrated with an example. Finally, the numerical results are plotted to show how memory effects affect ecological stability over time using iterative population estimates.