Fixed-point theorem for Caputo-Fabrizio fractional Nagumo equation with nonlinear diffusion and convection (Q2792636)

The aim of the paper is to prove the existence and uniqueness of solutions to the Nagumo differential equation by converting it to a fractional integral equation of Caputo-Fabrizio type. The author proves that the kernel of the integral satisfies Lipschitz condition and then considers an iteration method. Alas, it is not evident that what the parameters involving the equation exactly mean, what the definition of the exact solution is, to which fixed point theorem the author appeals to prove the existence of this kind of solution, and why the error estimate of the iterates tends to zero.