This paper presents a significant advancement in the study of stochastic partial differential equations within the context of nanobioscience, focusing on models that incorporate multiplicative noise. The main goal is to obtain precise solutions for these intricate equations, which is challenging due to the unpredictability brought about by stochastic elements. We utilize two advanced mathematical methods to achieve this: the refined Kudryashov’s technique and the -expansion strategy. These methods allow us to derive various new exact solutions, such as kink-type wave solutions, straddled solitons, and singular solitons. A unique aspect of our research is the integration of a white noise term into our model, significantly enhancing the theoretical framework for stochastic partial differential equations in nanotechnology. This integration provides a closer match to actual phenomena and creates opportunities to investigate the behavior of nanoscale biological processes influenced by stochastic factors. The solutions we have identified highlight the value of our model in offering more profound insights into the complex behaviors observed in nanoscience systems, facilitating further theoretical and applied investigations in this cross-disciplinary area.
