© 2022 Elsevier GmbHPurpose: In this study, we investigated the time-fractional coupled nonlinear Schrödinger (TF-CNLS) system in conformable fractional sense. TF-CNLS system models the circularly-polarized waves in the optic branch of physics frequently. Methodology: To obtain optical solitons of the model via new Kudryashov method and Kudryashov auxiliary equation methods have been applied. Findings: After implementing the mentioned methods on the model, we obtained bright, singular, W-shaped and bright soliton solutions. According to obtained soliton types, it is clearly seen that the methods are efficient and have ease of use. We depicted the results obtained by 3D and 2D graphs and investigated the wave motion according to the parameter and fractional order changes. Originality: We have applied a modulation instability to the TF-CNLS system for the first time. Due to literature research, we propose that this study is innovative and has novel inference.