From Biological Fractal Dynamics to Analog Fractional‐Order Circuits: A System Design Framework Based on Operatorization Thought

ABSTRACT

Fractional calculus, with its unique advantage in describing memory and nonlocal effects, has become a key tool for modeling nonlinear dynamic systems. Its integration with circuit systems has opened up a new paradigm for modern circuit design. However, the development of analog fractional‐order circuits (AFCs) is limited by the difficulty in physical implementation of ideal fractional‐order elements (fractances) and the lack of systematic design theories. Based on biological dynamics in physical fractal space and operatorization thought, this article aims to provide a novel approach to address the above challenges. The core work of this paper is to systematically introduce operatorization thought into the field of circuits and construct a universal fractional‐order system design framework applicable to multiple disciplines. Unlike traditional methods relying on backend optimization, this research focuses on the intrinsic construction of frontend fractional‐order systems. By deeply understanding the physical connotation of fractional‐order operators and leveraging the force‐electricity analogy principle, the approximation of fractional‐order circuits using classical integer‐order components is realized. Theoretical analysis and circuit simulations demonstrate that this method not only simplifies the design process but also reveals the inherent connection between fractional‐order circuits and fractal operators from a physical perspective, providing a solid theoretical basis and innovative path for the design of high‐performance, integrable fractal circuits.