A Practical Example of Fractional Order Application

This is a practical example demonstrating the application of fractional order systems. First, we provide the MATLAB implementation code for calculating the fractional Fourier transform. The code utilizes fractional calculus principles to handle non-integer order transformations, implemented through specialized algorithms like the Grünwald-Letnikov or Riemann-Liouville definitions. Next, we employ this code to compute power spectral density. Fractional order represents a mathematical concept distinct from integer order systems, allowing more accurate characterization of various phenomena such as complex signal behaviors and system dynamics. By applying fractional order techniques, we can achieve deeper insights into signal processing, control systems, and other engineering domains. In this specific example, we demonstrate how to calculate power spectrum using fractional order methods, which enables better understanding of signal frequency characteristics through enhanced spectral resolution. The implementation involves applying the fractional Fourier transform to time-domain signals followed by spectral estimation techniques. This example aims to provide a clear demonstration of fractional order applications, helping readers master this advanced concept through practical code implementation and result analysis.