On a New Modified Fractional Analysis of Nagumo Equation

Abstract

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo-Fabrizio and Atangana-Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.