Abstract
The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.
Highlights
Nowadays, the study of bio-mathematical models is considered as an original icon in the investigation of the dynamical and physical behavior of many biological models such as DNA [1], viruses [2, 3], the nerve system, the bacteria cell [4, 5] and their distribution, and the transmission of their impulses, and so on
We study the AB time-fractional FN equation [26, 27]
Applying the improved Riccati expansion method to the obtained ODE leads to many analytical solutions of this model
Summary
The study of bio-mathematical models is considered as an original icon in the investigation of the dynamical and physical behavior of many biological models such as DNA [1], viruses [2, 3], the nerve system, the bacteria cell [4, 5] and their distribution, and the transmission of their impulses, and so on. Many research papers have investigated the analytical and numerical solutions of the time fractional FN equation [28,29,30,31,32,33,34,35,36,37] for discovering novel properties of the transmission for the nerve impulses of a nervous system. These solutions are very useful tools for better understanding of the transmission attitude.
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