On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation

Recently Caputo and Fabrizio introduced a new derivative with fractional order. In this paper, we presented useful tools about the new derivative and applied it to the nonlinear Fisher's reaction-diffusion equation. We presented the solution of the modified equation using the notion of iterative method. Using the theory of fixed point, we presented the stability of the used method. Some numerical simulations were presented for different values of fractional order.