Human brain functions and behaviors during the transition state between sleep and wakefulness are not similar to these at alert wakefulness state. The transition state, which is called sleep inertia, has many unpleasant and dangerous effects on many situations that require full attention and fast response, such as driving. Within 30 minutes after waking up from sleep, the driver's performance might be impaired due to the sleep inertia effects. Groups of drivers that may drive within a short period after waking up are: workers who travel early in the morning; secondary drivers of long distance bus who sleep in the bus before taking over the job from the primary drivers; night travelers; and long haul truck drivers who stop at the rest area to sleep for a while and continue driving. Previous research used subjective self-report measurement, eye tracker, and a driving simulator to analyze the driver's performance during sleep inertia state. The physiological measures of the drivers, such as their brain signals have also been studied. However, the brain signals which are recorded in Electroencephalography (EEG) are typically analyzed in perspective of the power spectrum. This study proposes a hybrid of EEG features, which are fractal dimension and power spectrum, supported by behavioral data which is the driver's reaction time. This study finds the features that significantly differentiate between normal and sleep inertia drivers based on the classification accuracy and p-value of the statistical ANOVA. This study compares the results with other features (power spectrum, variance, sample entropy), and between EEG channel. This study record the EEG from the Fz, T7, Cz, Pz, and O1 channels. This study uses subjective and behavioral measurements to support the results. The results show that the hybrid of fractal dimension estimated by Katz's algorithm at the O1 channel and delta power from the Fz channel, and alpha power from the O1 channel, have better classifications than the power spectrum alone. Furthermore, the reaction time recorded from the LED reaction time task shows a significant difference between drivers with sleep inertia and normal (alert) drivers.