Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law

Abstract In the present paper, a new fractional order predator–prey model is considered. The applied fractional operator is a generalized Atangana–Baleanu–Caputo (ABC) derivative, which does not require any restrictions on the initial conditions as in the case of classical ABC fractional derivatives. On the theoretical aspect, we prove the existence, uniqueness, and Ulam–Hyers stability results by using some fixed point theorems and nonlinear analysis techniques. The numerical aspect discusses the approximation solutions for the proposed model by applying the generalized scheme of the Adams–Bashforth technique. At the end, we explain the behavior of the solution to the studied model through graphical representations and numerical simulations.