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.