Abstract
We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme.