<p>This paper analyzes the extended (3+1)-dimensional nonlinear conformable Schrödinger equation in a dispersion and nonlinearity managed fiber laser. To derive several new optical soliton solutions for the model, we employ two distinct Kudryashov methods, one of which is improved and enhanced in this study, resulting in a novel approach introduced to the literature. The importance of these newly obtained optical solutions is illustrated through contour, three-dimensional, and two-dimensional graphs, which depict the formation of kink-type waves and dark solitons. Furthermore, the effects of the conformable derivative parameter and the temporal parameter on these solutions are analyzed, providing valuable insights into the conformable nonlinear Schrödinger model. The algorithms developed in this study show promise for broader applications across various nonlinear Schrödinger equations in fields such as applied mathematics and nonlinear optics. Additionally, this research suggests that these methods could be extended to investigate other differential equations, both fractional and integer, in diverse areas of applied science.</p>