On the Traveling Wave Solutions of the Fractional Diffusive Predator—Prey System Incorporating an Allee Effect

We consider a system of two fractional-derivative order partial differential equations which describes the dynamics of predator-prey communications where the prey as well as the predator are subjected to an Allee effect. Using fractional traveling wave 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 traveling wave solutions of the reduced system. We present the solutions of the system equations (for the prey and for the predator) as finite series of the solutions of two different simple equations. One of obtained solutions is simulated numerically and the visualized traveling waves of the prey and the predator population densities are analyzed.