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This present study examines the closed-form wave results (CFWRs) of the nonlinear time-fractional model (NLTFM) with Atangana’s conformable fractional derivative (ACFD) through the unified process. ACFD and its properties are included. Then, by proposing the studied approach, the CFWRs of NLTFMs, displayed with the ACFD, are classified. This model defines the transmission of optical solitons in physics and applied mathematics and may be acute to the soliton waves. A lot of new CFWRs have been gained. For a few parameter values involved in the answer functions, physical behaviors on 3D graphics, contour graphics, and 2D graphics for the different values of αwere examined. We apply the unified process on the NLTFM model and provided thirty six CFWRs. Contrary, Y. Gurefe [40] studied the same model model to derive only five CFWRs. As results, our technique in the present paper provides abundant CFWRs. From the observation of the outcomes acquired, it is noticed that the studied process can generate essential effects in taking the closed-form wave results of NLTFMs containing ACFD.