  We consider a modified Lotka-Volterra model applied to the predator-prey
system that can also be applied to other areas, for instance the bank system.
We show that the model is well-posed (non-negativity of solutions and
conservation law) and study the local stability using different methods.
Firstly we consider the continuous model, after which the numerical schemes of
Euler and Mickens are investigated. Finally, the model is described using
Caputo fractional derivatives. For the fractional model, besides well-posedness
and local stability, we prove the existence and uniqueness of solution.
Throughout the work we compare the results graphically and present our
conclusions. To represent graphically the solutions of the fractional model we
use the modified trapezoidal method that involves the modified Euler method.

Dynamical Systems;Numerical Analysis;Numerical Analysis