Model-Driven Applications of Fractional Derivatives and Integrals

TL;DR

This paper explores fractional derivatives and integrals from a frequency-domain perspective, offering a computational framework and applications for signal processing using Riesz formalism.

Contribution

It introduces a frequency-domain approach to fractional differintegrals, generalizing classical operators with practical computational tools and applications.

Findings

Provides a frequency-domain interpretation of fractional differintegrals.

Demonstrates applications to 1D and 2D signals.

Offers computer code for implementation.

Abstract

Fractional order derivatives and integrals (differintegrals) are viewed from a frequency-domain perspective using the formalism of Riesz, providing a computational tool as well as a way to interpret the operations in the frequency domain. Differintegrals provide a logical extension of current techniques, generalizing the notion of integral and differential operators and acting as kind of frequency-domain filtering that has many of the advantages of a nonlocal linear operator. Several important properties of differintegrals are presented, and sample applications are given to one- and two-dimensional signals. Computer code to carry out the computations is made available on the author's website.