A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Abstract This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator prey act as agents in an ecosystem this simulation. We focus on order Atangana–Baleanu operator the sense Liouville–Caputo. Due nonlocality method, generated by using another FO derivative developed kernel based generalized Mittag-Leffler function. Two fractional-order systems are assumed, without delay. For numerical solution models, we not only employ Adams–Bashforth–Moulton method but also explore existence uniqueness these schemes. use fixed point theorem which useful describing new approach particular set solutions. illustration, several examples added show effectiveness method.