On certain exact solutions of diffusive predator-prey system of fractional order

Partial differential equations are used to model the variety of ecological phenomena and also extensively applied to elucidate the effects of spatial variation on populations. This paper investigates the issue of exact solutions for some important population growth dynamic models of fractional order. More precisely, a system of equations for description of the predator-prey relations and reaction-diffusion invasion model is considered. In particular, the predator-prey model corresponds to the modified Lotka-Volterra system with logistic growth of predator and prey. Exact traveling wave solutions of the considered models are found by means of the Q-function method. Moreover, graphical illustrations of some of the obtained solutions in two and three dimensional are also provided to predict their behavior dependence on the parameter values. The results reveal that the Q-function method is very simple, reliable and effective for finding exact solutions of complex nonlinear evolution equations.