A novel piece-wise approach to modeling interactions in a food web model

New definitions always have more capabilities in describing phenomena than the more classic and well-known concepts because they usually appear to fill the gaps in existing concepts. In this paper, we employ a new stochastic fractional system that models interactions in a mutualism–parasitism food web. The main idea of piece-wise differential and integral operators is to separate the time under study into separate time domains in which the model behaves different behaviors. The idea was recently proposed by Atangana et al., and is gradually being used to solve a variety of application models. In order to demonstrate the valuable capabilities of this approach, many numerical simulations are provided in this paper. These results are mainly obtained from studying the role of the parameters in the model on its overall behavior. The results confirm that the piece-wise approach to the problem is a wise idea with more effectiveness rather than considering the whole situation is studied by a single operator. It is recommended to use these modified operators in modeling other applied problems with similar features.