Fractional-Order Three-Dimensional $\nabla \times n$ Circuit Network

This paper introduces new fundamentals of the three-dimensional ∇×n RLC circuit network in the fractional-order domain. First, we derive the general formula of the typical equivalent impedance of the circuit network in different cases by using matrix transform method and the difference equation model. Then, we systematically investigate the effects of the five system parameters (inductance (L), capacitance (C), the number of circuit units (n), and fractional orders α and β) on the impendence characteristics and the phase characteristics of two different cases. Specifically, interesting phenomena and laws are presented by the numerical simulations. Moreover, a comparative analysis about the impendence characteristics and the phase characteristics of the two cases for the fractional-order three-dimensional circuit network is studied in detail. Finally, the results of PSpice simulation are presented to validate the study.