Analytical approximations for a population growth model with fractional order

In this paper, we apply the homotopy analysis method (HAM) to solve the fractional Volterra’s model for population growth of a species in a closed system. This technique is extended to give solutions for nonlinear fractional integro–differential equations. The whole HAM solution procedure for nonlinear fractional differential equations is established. Further, the accurate analytical approximations are obtained for the first time, which are valid and convergent for all time t. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional integro–differential equations.