Numerical Simulation of Nonlinear Ecological Models with Nonlocal and Nonsingular Fractional Derivative Kolade M. Owolabi 1 Introduction Over the years, the subject of ecology has been studied and becomes day-in and day-out activities. The meaning of ecology has gone beyond monitoring a flock of animals. In population dynamics, it has been used to address the interpersonal relationship between two or more species, where a functional response of the higher species (predator) to that of the lower species (prey) is known to be the change in the density of prey attached per unit time per predator as the prey density changes. Different types of functional response used to model various predation scenarios have been reported in [20, 21] to compliment the realistic standard Lotka–Voltera system. Zhang et al. [35] study the effect of periodic forcing and impulsive perturbations on predator–prey system with Holling type-IV functional response. In contrast to the classical single or multicomponent species dynamics that were extensively reported in literature between the 1970s and 1980s and till date, respec- tively [19], predator–prey systems are known to give rise to period and spatiotemporal oscillations. Though most systems with steady-state equilibria often result to oscil- latory transients with a stable frequency. Many (fluctuating) population scenarios appear to be modelled by such interactions. Nonetheless, fractional predator–prey models have been poorly reported with respect to the interaction of nonlinear dy- namics. The total population of the mathematical model can be denoted by P, which is subdivided into two or three groups, that is, a group referred to as the prey on which the higher class depends for existence. The second group contains the species K. M. Owolabi (B ) Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, University of the Free State, Bloemfontein 9300, South Africa e-mail: koladematthewowolabi@tdtu.edu.vn Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam © Springer Nature Singapore Pte Ltd. 2020 H. Dutta (ed.), Mathematical Modelling in Health, Social and Applied Sciences, Forum for Interdisciplinary Mathematics, https://doi.org/10.1007/978-981-15-2286-4_10 303