Solitary wave solutions of Fitzhugh-Nagumo-type equations with conformable derivatives

Abstract

The Fitzhugh-Nagumo equation is an important non-linear reaction-diffusion equation used to model the transmission of nerve impulses. This equation is used in biology as population genetics; the Fitzhugh-Nagumo equation is also frequently used in circuit theory. In this study, we give solutions to the fractional Fitzhugh-Nagumo (FN) equation, the fractional Newell-Whitehead-Segel (NWS) equation, and the fractional Zeldovich equation. We found the exact solutions of these equations by conformable derivatives. We have obtained the exact solutions within the time-fractional conformable derivative for these equations.