This paper secures optical solitons with fractional temporal evolution in presence of a few perturbation terms. The extended G'/G-expansion method reveals bright, dark and singular soliton solutions to the model. The study is conducted with four forms of nonlinear media. The results will be useful to conduct slow evolution of pulses in an optical fiber for controlling Internet bottleneck. (C) 2018 Elsevier GmbH. All rights reserved.