The charge carrier mobility is an important parameter to characterize the performance of organic semiconductors based optoelectronic devices. In a given organic semiconductor, the mobility is often calculated based on the space-charge-limited (SCL) current measurement by fitting the corresponding current-voltage (J-V) data with a range of available space-charge-limited transport models to achieve the best fit, however, the accuracy of extracted mobility parameter relies on the correctness of model being used. Here, we present a fractional-dimensional SCL transport model for organic semiconductors with spatial disorder based on the fractional-dimensional calculus approach. We show that the thickness scaling of the SCL current is related to the spatial disorder in organic devices. The fractional-dimensional SCL transport model agrees well with the measured current density of several organic diode devices. The reported model is able to extract mobility values in organic devices with better accuracy as compared to existing models in the literature.