Class Description for Fractional-Order Transfer Functions

This section provides a comprehensive description of the fractional-order transfer function class, covering its definition, properties, and practical applications. Fractional-order transfer functions serve as essential mathematical tools for characterizing the dynamic behavior of signals and systems. The implementation includes methods for generating Bode plots and Nyquist diagrams, which are crucial for analyzing system stability and frequency response characteristics. From a coding perspective, key functions typically involve fractional-order differentiation/integration operators (e.g., using Grünwald-Letnikov or Caputo definitions) and frequency domain analysis algorithms. We will also introduce fundamental concepts of fractional calculus and their practical applications to help readers better understand the intrinsic nature of these class functions, including numerical implementation considerations for handling non-integer orders through discrete-time approximations.