Solitary Wave Structures for Time Fractional Stochastic Poisson-Nernst-Planck Model in Electrobiochemical System

This study focuses on solitary waves for the time-fractional stochastic Poisson Nernst-Planck equation arising in the movement of ions in electrolyte solutions. The Nernst-Planck equation is coupled with the Poisson equation that describes the electrostatic potential. We study the improved F-expansion method, the modified extended tanh-function method, and the polynomial expansion method to analyze the fractional model. We derive various new solutions that exhibit distinct behaviors. The results demonstrate that these strategies are robust, reliable, and efficient tools for tackling complex models in applied sciences. The solutions are expressed in trigonometric, exponential, and hyperbolic functions. We present three-dimensional, two-dimensional, and contour plots of selected solutions to illustrate the impact of multiplicative time noise and mean time dynamics. These plots visually capture the effect of randomness on the wave structure of the precise outcome for solitary wave solutions.