- - - Dep. of Applied Mathematics, Yadegar-e-Imam Khomeini (RAH), Shahr-rey Branch, Islamic Azad University, Tehran, Iran.
- - - Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
- - - Dep. of Applied Mathematics, Yadegar-e-Imam Khomeini (RAH), Shahr-rey Branch, Islamic Azad University, Tehran, Iran.

‎The Lotka-Volterra model is an important model being employed in biological phenomena to investigate the nonlinear interaction among existing species‎. ‎In this work‎, ‎we first consider an integer order predator-prey model with negative feedback on both prey and predator‎. ‎Then by introducing a fractional model into the existing one‎, ‎we give them a specified memory‎. ‎We also obtain its discretized counterpart‎. ‎Finally‎, ‎along with giving the biological interpretation of the system‎, ‎the stability and dynamical analysis of the proposed model are investigated and the results are illustrated as well‎.

Fractional calculus, Predator-prey, Lotka-Volterra, Stability, Discretization