Optimization and dynamics of non-integer food chain model with three-species

Food chain integrity is a multi-disciplinary aspect from producers to consumers; this is because food chain, food safety, and food-processing sectors have new challenges due to globalization of microbial and chemical food safety from fraud to quality. In this context, a new fractional-fractal non-integer differential chaotic dynamical food chain model is developed with dynamical behavior and functional responses. A comparative study is investigated with sensitive parameters through numerical simulations of non-integer differentiations. The equilibrium points with local and asymptotical stability have been established through Jacobian matrix method for exhibiting more complicated dynamics within the feasible imposed conditions. To check the sensitivity of food chain model, the parametric values are chosen for the intrinsic properties (growth rate, the death rate, predation rate, conversion rate, and the maximal growth rate) of food chain model. Finally, the interference between prey and intermediate predator is investigated via chaotic.