Abstract
In this paper, the Adomian's decomposition method has been developed to yield approximate solution of the reaction-diffusion model of fractional order which describe the evolution of the bacterium Bacillus subtilis, which grows on the surface of thin agar plates. The fractional derivatives are described in the Caputo sense. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional order.