针对Oldham RC分形链类的电路特征，给定初始阻抗，采用 3种方法理论推导 Oldham分形链类阻抗函数解析表达式，并对比分析各求解方法。根据 Oldham分形链分抗逼近电路的连分式表示和连分式三项递推公式，引入阻抗函数新的数学表示形式：连分式三项递推矩阵。通过分析Liu-Kaplan标度迭代电路和标度方程，推导出 2种Liu-Kaplan分形链类阻抗函数的数学表示形式。通过理论验证和实验仿真对比不同分数阶下的阻抗函数表达式和频域特征与运算特征曲线。

Aiming for the circuit characteristics of the Oldham RC fractal chain, the analytical expressions of Oldham RC fractal chain impedance function are deduced by using three methods at given initial impedances. Then, the solution methods are compared and analyzed. According to the continued fractional representation of the approximation circuit of Oldham fractal chain fractance, and the three-term recurrence formula of continuous fraction, a new mathematical representation of impedance function is introduced: continuous fractional three-term recursion matrix. By analyzing the Liu-Kaplan scaling iteration circuit and the scaling equations, two mathematical representations of the impedance functions of Liu-Kaplan fractal chains are deduced. Theoretical and experimental simulations compare the impedance function expressions and frequency characteristics of different fractional orders.