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.

由Atangana-Baleanu（AB）时间分数FitzHugh-Nagumo（FN）方程以数学方式公式化地表示了神经系统神经冲动的传递动力态，并通过两种不同的方案进行了计算和数值研究。这些方案是改进的Riccati展开方法和B样条方案。此外，基于哈密顿量的特征说明了分析评估解决方案的稳定性，以解释它们在模型应用中的适用性。此外，通过在三种不同类型的图中绘制草图，可以弄清所获得解决方案的物理和动力学行为。显示了所应用方法的实用方面和优势，以解释其在许多其他非线性评估方程中使用的能力。