The Replacement of Lotka-Volterra Model by a Formulation Involving Fractional Derivatives

This paper proposes a generalization to the Lotka-Volterra system utilizing fractional derivates. The aim of this generalization is to improve the description of the phenomenon in an analogous way to the one that was made in recent works concerning viscoelastic systems, such as human blood. The classical predator-prey model, i.e., the Lotka-Volterra system with derivatives of integer order is discussed and, using a linearization technique, a solution is obtained in terms of the constant parameters. In addition, a solution of the so-called Lotka-Volterra fractional differential system, which is a system of two non linear fractional differential equations where each fractional derivative has order lower than one, is obtained in terms of the Mittag-Leffler function, using the Laplace transform methodology associated with the linearization technique.