In this work, the dynamics of dephasing (without relaxation) in the presence of a chaotic oscillator is theoretically investigated. The time-dependent density functional theory framework was used in tandem with the Lindblad master equation approach for modeling the dissipative dynamics. Using the Kohn-Sham (K-S) scheme under certain approximations, the exact model for the potentials was acquired. In addition, a space-fractional K-S scheme was developed (using the modified Riemann-Liouville operator) for modeling the dephasing phenomenon. Extensive analyses and comparative studies were then done on the results obtained using the space-fractional K-S system and the conventional K-S system. © 2014 Wiley Periodicals, Inc.