<p>Fractional calculus has advantages such as heritability and memory, which enable it to better describe the characteristics of systems, thus attracting increasing attention from researchers. Due to the diversity and complexity of the electrical components contained in circuit systems, there is currently more discussion about their ideal state, i.e., no loss, which is difficult to achieve in reality. Therefore, using fractional calculus to describe circuit systems will be more accurate. This article mainly studies the circuit system in two steps to achieve the derivation of equivalent fractional-order (FO) circuit systems and the design of synchronization control schemes. Firstly, for the components in the circuit, fractional operators is applied to describe the relationship between current, voltage, capacitance, etc. Furthermore, based on the relationship between variables, an equivalent model of FO circuit systems is derived. Secondly, based on the event-triggered mechanism, synchronization control schemes are designed for the obtained FO circuit system with the same orders and different orders. Specifically, the method used to derive FO circuit systems is a universal approach that can be extended to other circuit models, and the designed control scheme not only includes synchronization between systems with the same order, but also between system with different orders, which helps to better describe synchronization phenomena. Finally, two simulation examples are provided to verify the effectiveness of the proposed scheme.</p>