Abstract
This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana-Baleanu-Caputo derivative with fractional order. Also, using the well-known Adam-Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model.