Abstract
In this paper, the variational iteration method is presented for the numerical solutions of the generalized reaction-diffusion models for bacterial growth. The fractional derivatives are described in the Caputo sense. Linear stability analysis of the deterministic system has been studied. The results show that the solution continuously depends on the time-fractional derivative. The resulting solutions of fractional order spread faster than the classical solutions. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional order.