The objective of this work is to model a population management in which two species intervene. There is an interdependence predator-prey relationship between them. It will be assumed, as a descriptive biological model, the Lotka-Volterra one with the application of an Allee effect in one of the dynamics of the species. This incorporation into the system make the model more realistic.
In view of the advantages, the model will be in its fractional version, that is, where derivatives of Caputo of fractional order are considered, with the fractional order in (0,1]. Existence and uniqueness of the model solution will be explicitly proved, and a non-negative invariance of the solution and the stability of the resulting equilibrium will be studied. In order to solve the problem, the use of fractional numerical techniques will be of fundamental importance and absolutely essential to conclude the analysis. Some examples of great importance will be shown.