The Impact of Fractional Derivatives with Singular and Non-Singular Kernels on the Dynamics of Holling Type II Predator–Prey Models Under Climate Change Effects

This work investigates the complex dynamics of two novel Holling type II predator–prey (PP) models under the impact of climate change and controlled by the Caputo and Caputo–Fabrizio fractional operators. Here, Holling type II and static changes are considered using the first PP model, while the other PP model is considered when periodic changes over time are employed. In the presence of each fractional operator, the stability analysis of all equilibrium states is studied, and the conditions of asymptotically stability are obtained. The numerical results showed considerable variability in the complex dynamics of these models using both operators. Furthermore, a comparison of the numerical results showed that the Caputo–Fabrizio operator is better than the Caputo operator in describing the complex dynamics of the second model because the scenarios displaying chaos regions when using the Caputo–Fabrizio operator occur over wider ranges than their counterparts when using the Caputo operator. With the memory effect present, the results show an improvement in system stability and thus an increased survival possibility despite the presence of adverse climatic conditions in the environment.