The nonlinear fractional soliton neuron model is an important part of many complex fields, such as fluid mechanics, applied science, neuroscience, nonlinear dynamics, mathematical physics, engineering, biosciences, plasma physics, and geochemistry. It shows how nonlinear waves propagate. This paper uses a thermodynamic theory of neural signal transmission to show how the suggested model works, what it can do, and how it might work as it moves along axons. To solve this model, we first convert the partial differential equation form to the ordinary differential equation form. We then use the φ6-model expansion scheme to determine the wave profiles for the above-stated equation. We manufactured 2D and 3D density plots and different types of soliton solutions with the help of computational software. Additionally, we illustrated a sensitivity analysis of the mentioned nonlinear problem using planner dynamics. The results of different solitons show that the suggested method works very well and is perfect for dealing with the soliton solutions of nonlinear equations. This makes it especially useful for studying complicated wave phenomena in many scientific areas.
Rahaman et al. (2025) studied this question.