Several Exact Solutions of the Fractional Predator—Prey Model via the Simple Equations Method (SEsM)

We consider a system of two fractional-derivative order partial differential equations which describes the dynamics of predator-prey communications where the prey per capita growth rate is a subject to an Allee effect. Using conformable fractional transformations, the fractional-derivative order partial differential equations are converted to ordinary differential equations with integer order. We apply the Simple Equations Method (SEsM) for obtaining exact analytical solutions of the reduced system. We present the solutions of the system equations as finite series of the solutions of two different simple equations. One of obtained solutions is simulated numerically and is analized in the context of predator—prey dynamics.