Lie symmetry analysis and exact solutions of the time-fractional biological population model

Abstract

We first perform a complete Lie symmetry classification for the time-fractional biological population model with Riemann–Liouville fractional derivative and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the F-expansion method and the reduced equations, we obtain several new exact solutions for the equation and show the propagation pattern via the evolutional figures. By means of the power series theory, an exact power series solution of the equation is also constructed.