We use the nonlinear Schrödinger equation (NLSE) describing the polarization mode in optical fiber (OF) with Self-Steepening (SS), Self-Frequency Shift (SFS) and Cubic-quintic (CQ) term to analyze the effects of the fractional time parameter (FTP) on propagation of the breather-like solitons. We show the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as on the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected. Moreover, we show the effects of fraction time (FT) on Modulation Instability (MI) gain spectra. For all values of the FP, side lobes are formed and when these values increase the stability zones increases and the amplitude also increases values and the stability zones increases, both the stability zones and the soliton amplitude increase. We numerically investigate the propagation of the continuous waves (CW). We show the formation of stable breather-like soliton for small values of the FTP.