A General Study on 3D Fractional Order Hexagonxn x n RLαCβ Circuit Network

This paper studies the electrical conductivity of a conductive material with structures similar to graphene, which consists of three basic components. The influence of various factors on the electrical conductivity of the fractional order is also analyzed. Moreover, the new fundamentals of the hexagon x n RL alpha C beta circuit network in the fractional domain are introduced, and the general laws are summarized. First, we derive three general formulas of the equivalent impedance (Z(AD)(n), Z(BC)(n), and Z(AA)(')(n)) of the circuit network by using the matrix transform method and the difference equation model in a special case. In addition, taking Z(AA)(') (n) as an example, we systematically investigate the effects of the seven system parameters (frequency omega, the number of circuit units n, fractional order alpha for inductance, fractional order beta for capacitance, inductance L, capacitance C, and resistance R) on the impedance characteristics of the 3D fractional order circuit network. Specifically, interesting phenomena and laws are shown by visual figures.

Automated summary

This paper studies the electrical conductivity of a conductive material with structures similar to graphene and analyzes the influence of various factors on the electrical conductivity of the fractional order. It also introduces the new fundamentals of the hexagon x n RL alpha C beta circuit network in the fractional domain and summarizes the general laws.