In order to analysis the fractional reaction-diffusion equation or non-homogeneous heat equation , we use Caputo– Fabrizio(CF) fractional derivative. The solution of reaction diffusion equation describes that how the heat propagate in the medium. The existence – uniqueness of the model solution are discussed using the method of fixed point theorem. Finally numerical approximation are performed with the help of Homotopy Analysis Method(HAM). Effect of heat propagation depends on order of the equation and memory of the kernel are shown by comparing the Caputo-Fabrizio and Caputo sense of derivative. Graphical presentations of solution are shown to observe some unusual irregularities of the equation for time fractional derivatives with singular and non-singular kernels.