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We make use of fractional derivative, recently proposed by Caputo and Fabrizio, to modify the nonlinear Nagumo diffusion and convection equation. The proposed fractional derivative has no singular kernel considered as a filter. We examine the existence of the exact solution of the modified equation using the method of fixed-point theorem. We prove the uniqueness of the exact solution and present some numerical simulations. c ©2016 All rights reserved.

Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection