This article presents the results of theoretical and experimental study of fractional Bennet\'s electricity multiplier based on Dickson charge pump topology. This network is used for conditioning of capacitive transducers in kinetic energy harvesters. This study investigates of the operation of the circuit in purely electrical mode (no electromechanical coupling), addressing the transient processes and influence of the parameters\' values on the circuit behaviour. Several original results have been obtained: existence of three different transient processes, strong qualitative influence of the diode\'s threshold comparing with ideal behavior and stability criterion on one of the transient processes. These results provide useful insight into the operation of the circuit and are of practical interest for the application of this circuit. The analysis is validated by Spice simulation and by measurements performed on a MEMS silicon device.