Journal of Research in Electrical Circuits and Systems ISSN: 3139-2059 (Online)

Authors: Dr. Meera V. Reddy, Dr. Subhankar K. Roy

Abstract: Fractional-order calculus (FOC) has emerged as a powerful mathematical framework for modeling, analysis, and control of electrical circuits that exhibit memory and hereditary properties. Unlike conventional integer-order
models, fractional-order models can accurately capture complex dynamics in resistive, capacitive, and inductive elements, especially in lossy, dispersive, or bioelectrical systems. This paper reviews circuit modeling using fractional-order calculus, highlighting theoretical foundations, design methodologies, simulation techniques, and applications in analog filters, control circuits, and
bioelectronic devices. Tables summarize typical fractional-order elements and their characteristics, while a 2D block diagram illustrates a generalized fractional-order circuit modeling approach. Challenges, such as numerical
implementation and stability analysis, are discussed, alongside future research directions.

Keywords: Fractional-order calculus, Fractional-order circuits, Electrical modeling, Analog filters, Control systems, Bioelectronics, Memory effects