New Exact Traveling Wave Solutions of Fractional Time Coupled Nerve Fibers via Two New Approaches

Abstract

In this paper, we obtain new soliton solutions of one of the most important equations in biology (fractional time coupled nerve fibers) using two algorithm schemes, namely, $\exp \left(-\psi \left(\xi \right)\right)$ expansion function method and $\left({\theta }^{\prime }\left(\xi \right)/{\theta }^2\left(\xi \right)\right)$ expansion methods. The equation and the solution methods have free parameters which help to make the obtained solutions are dynamics and more readable for dealing with fractional parameter and the initial and boundary value problem. As a result, various new exact soliton solutions for the considered model are derived which include the hyperbolic, rational, and trigonometric functions, and other solutions are obtained. In addition, the obtained results proved that the used methods give better performance compared with existing methods in the literature.