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 − ψ ξ expansion function method and θ ′ ξ / θ 2 ξ 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.
Highlights
Differential equations attained great importance with several applications in nature and live environment [1–19]
We propose a system which is governed by a fractional order derivative. e fractional order derivative is a concept that has been known since the early 17th century [43–45]. e model studied here is the ephaptically coupled myelinated nerve fibers. e myelinated nerve fibers might be responsible for diagnostic dilemmas in cases of visual loss [46–48]. ey allow an increase in the speed of a nerve impulse while decreasing the diameter of the nerve fiber. e first work concerning myelinated nerve fibers was developed by Rushton [49]
We introduced new solutions to one of the most important differential equations in biology
Summary
Differential equations attained great importance with several applications in nature and live environment [1–19]. Several studies have attempted to provide an interpretation to the nature of the nerve conduction. Is study presents a model of action potential propagation in bundles of myelinated nerve fibers. E nature of the conduction process on an isolated nerve axon is studied numerically and compared with the theoretical models [24]. We propose a system which is governed by a fractional order derivative. E model studied here is the ephaptically coupled myelinated nerve fibers.
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