Figure 1

Numerical simulation for the prey–predator model via Atangana–Baleanu–Caputo fractional derivative with constant order (2.1) via the numerical scheme given by Eq. (3.22). In (a)–(b) phase portrait and time series \(\mathbf{x}(\tau )\) and \(\mathbf{y}(\tau )\) for \(\epsilon =1\) and \(\varsigma =1\). In (c)–(d) phase portrait and time series \(\mathbf{x}(\tau )\) and \(\mathbf{y}(\tau )\) for \(\epsilon =0.95\) \(\varsigma =0.9\). In (e)–(f) phase portrait and time series \(\mathbf{x}(\tau )\) and \(\mathbf{y}(\tau )\) for \(\epsilon =0.9\) and \(\varsigma =0.95\)