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This article focuses on securing distinct optical solitons to optical fiber with the coupled nonlinear Schrödinger equation. The examined equation is analyzed with the aid of conformable space–time fractional and is known to have a significant role in the propagation of pulses through a two-mode optical fiber and the soliton wavelength division multiplexing. The fractional nonlinear partial differential equations have garnered increased interest since they may be utilized to explain a wide range of complicated physical phenomena and have more dynamic structures of localized wave solutions. New extended direct algebraic method, a relatively recent integration tool, is used to obtain the solutions. The diverse pulses as bright, dark, combo, and singular soliton solutions have been extracted. In addition to aiding in the clarification of fractional nonlinear partial differential equations, the employed method provides previously extracted solutions and extracts new exact solutions. Given the correct parameter values, numerous graph forms are sketched to provide information on the visual presentation of the obtained findings. The achieved solutions are to be attractive to researchers for understanding the complexity of the considered model. The findings of this research validate the effectiveness of the proposed method for increasing nonlinear dynamical behavior. It is anticipated that, the research will be of interest to all engineers who work with engineering models. Results demonstrate the efficacy, simplicity, and generalizability of the selected computational method. [ABSTRACT FROM AUTHOR]