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This paper presents the optimum control interval for intra-cell fractional transmission power control (TPC) for a shared data channel employing frequency domain channel-dependent scheduling and adaptive modulation and coding (AMC) in the evolved UTRA uplink using single-carrier (SC)-FDMA radio access. The simulation results show that the best attenuation factor in the fractional TPC is approximately 0.6 for achieving the maximum user throughput when the maximum target received signal power, P0 is -60 dBm. Then, we show that the optimum averaging interval for the desired signal level, which corresponds to a substantial control interval for the fractional TPC, is approximately 100 - 200 msec regardless of the maximum Doppler frequency up to 222 Hz and the distance at the shadowing correlation of 0.5. Throughout the simulation results, we verify that slow intra-cell fractional TPC associated with fast AMC is effective in achieving the maximum cell throughput and cell-edge user throughput.