An improved model along with a spectral numerical simulation for fractional predator–prey interactions

Predator–prey models appear in various fields of bio-mathematics used for the analysis of interactions of biological systems. Due to the complexities of the physical context for the real-world problems of food chain dynamics, introducing new models compatible with experimental results stays ongoing research. Many models have been proposed and analyzed for these systems in recent years. In this paper, we propose a new fractional-order predator–prey model with negative feedback on both species with memory-dependent effects, which increases the compatibility level of the model. Then we present a novel Laguerre spectral numerical simulation for the proposed model by introducing Laguerre modal basis functions with collocation and Galerkin techniques. We then transfer the nonlinear model into a system of algebraic equations, which is solved by efficient numerical solvers. Finally, we provide some test problems to show the efficiency of the proposed model and the computational method.