Two-sided fractional derivatives

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Abstract

In previous chapters the causal and anti-causal fractional derivatives were presented. An application to shift-invariant linear systems was studied. Those derivatives were introduced into four steps: 1. Use as starting point the Grünwald-Letnikov differences and derivatives. 2. With an integral formulation for the fractional differences and using the asymptotic properties of the Gamma function obtain the generalised Cauchy derivative. 3. The computation of the integral defining the generalised Cauchy derivative is done with the Hankel path to obtain regularised fractional derivatives. 4. The application of these regularised derivatives to functions with Laplace transform, we obtain the Liouville fractional derivative and from this the Riemann-Liouville and Caputo, two-step derivatives.

Original languageEnglish
Title of host publicationFractional Calculus for Scientists and Engineers
Pages101-121
Number of pages21
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Electrical Engineering
Volume84 LNEE
ISSN (Print)1876-1100
ISSN (Electronic)1876-1119

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