Abstract
In this research work, we employ the unified method, the extended sinh-Gordon equation expansion method (ShGEEM), and the extended rational sine-cosine/sinh-cosh method to derive the novel optical solitons solutions of the (2+1)-dimensional nonlinear dynamical conformable fractional generalized Schrödinger system in monomode optical fibers. We extract the optical soliton solutions in diverse forms like, dark, bright, combinations of dark-bright, periodic, and singular solutions, that are presented by trigonometric functions, and hyperbolic functions. The employed procedures are useful in order to clarify nonlinear partial differential equations (NLPDEs) and secure new exact solutions in addition to previously recovered ones. The accuracy of these answers has been verified for all extracted results using the Mathematica. The 3D surface plots, 2D line plots, and associated contour graphs are used to analyze the obtained solutions to visualize and support the theoretical conclusions using appropriate parameter values. The findings of this research demonstrate the efficacy of the approaches exploited in enhancing nonlinear dynamical behavior.