<p>This study presents several novel optical soliton solutions for the generalized derivative nonlinear Schrödinger equation under the influence of multiplicative white noise. To construct soliton solutions for the present model, two robust analytic algorithms, namely the new direct mapping method and the Kudryashov method, are employed. Using these methods, we derive a variety of solutions, including solitary wave solutions, bright solitons, dark solitons, singular soliton, and W-shaped soliton solutions. The main purpose of this paper is to construct various new optical soliton solutions and investigate their dynamical behavior under the influence of multiplicative white noise. This study presents an innovative approach by incorporating white noise impacts into the analysis of optical solitons, marking a significant advancement in exploring nonlinear wave phenomena. Driven by the far-reaching applications of the nonlinear Schrödinger equation over various scientific domains and the pivotal role of multiplicative white noise, the research includes carefully designed contour, three-dimensional, and two-dimensional graphs to effectively illustrate the influence of white noise on the derived soliton solutions.</p>