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arXiv · 1405.1999

Model-Driven Applications of Fractional Derivatives and Integrals

William A. Sethares·Selçuk Ş. Bayın
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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.

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William A. Sethares, Selçuk Ş. Bayın. 2014-03-21. Model-Driven Applications of Fractional Derivatives and Integrals. https://arxiv.org/abs/1405.1999

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