Infinite Energy Problem of Fractional Circuit Elements: Overview and Perspectives

Fractional circuit elements become increasingly popular due to their versatility in various applications. However, the bottleneck in deploying these tools in practice is related to an open problem, i.e, infinite energy problem. On this topic, many valuable achievements have been made. Some scholars don’t dare to use fractional circuit elements because of the infinite energy problem while some scholars believe that there is no paradox compared with classical finite energy or even some scholars think that this problem has been successfully solved. However, there is still no consensus on this topic and confusion remains widespread. Consequently, a comprehensive review on infinite energy problem is needed imperatively. At this point, this paper reviews the consequences, root causes, and potential mitigation approaches through the modeling analysis and literature survey. This review starts with the fractional capacitors. Subsequently, other fractional circuit elements and fractional order operators/systems are considered. Finally, the main technical challenges as well as future researches on this topic are highlighted carefully.