In road transportation systems, differential plays an important role in preventing the vehicle from slipping on curved tracks. In practice, mechanical differentials are used, but they are bulky because of their increased weight. Moreover, they are not suitable for electric vehicles, especially those employing separate drives for both rear wheels. The electronic differential constitutes recent technological advances in electric vehicle design, enabling better stability and control of a vehicle on curved roads. This article articulates the modeling and simulation of an electronic differential employing a novel wavelet transform controller for two brushless DC motors ensuring drive in two right and left back driving wheels. Further, the proposed work uses a discrete wavelet transform controller to decompose the error between actual and command speed provided by the electronic differential based on throttle and steering angle as the input into frequency components. By scaling these frequency components by their respective gains, the obtained control signal is actually given as input to the motor. To verify the proposal, a set of designed strategies were carried out: a vehicle on a straight road, turning right and turning left. Numerical simulation test results of the controllers are presented and compared for robust performance and stability.