International Journal of Engineering and Technology

In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional orders as well as different coefficients of population growth model. This indicates the validity and great potential of the shifted Legendre polynomial method for solving nonlinear fractional integro–differential equations.