Method of separation variables combined with homogenous balanced principle for searching exact solutions of nonlinear time-fractional biological population model

Avoided an invalid fractional chain rule, based on the method of separation variables, two forms of exact solutions of a nonlinear time-fractional PDE are supposed, and then combined with the homogenous balanced principle, we introduced a combination method for searching exact solutions of nonlinear time-fractional PDEs. By using this new method, a nonlinear time-fractional PDE, a biological population model is studied from mathematical viewpoint. Some new exact solutions of two forms of separation variables to this model are obtained. The dynamical properties of these exact solutions are discussed and the profiles of several representative exact solutions are illustrated.