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Analysis, Modeling and Stability of Fractional Order Differential Systems 1
book

Analysis, Modeling and Stability of Fractional Order Differential Systems 1

by Jean-Claude Trigeassou, Nezha Maamri
September 2019
Intermediate to advanced content levelIntermediate to advanced
316 pages
5h 39m
English
Wiley-ISTE
Content preview from Analysis, Modeling and Stability of Fractional Order Differential Systems 1

10Infinite State and Fractional Differentiation of Functions

10.1. Introduction

Fractional calculus has concerned the calculation of fractional integrals and derivatives for any kind of functions for a long time (see [OLD 72, MIL 93] and the references therein). Of course, integration of FDEs has also been an important issue, stimulated by physical and engineering applications [SAM 87, POD 99].

In the previous chapters, the infinite state approach was applied to the modeling and analysis of FDEs. In fact, this methodology also applies to other domains of fractional calculus, and particularly to the calculation of the fractional derivative of a function g(t), i.e. to images. This derivative depends on the differentiation technique used: Riemann–Liouville, Caputo or Grünwald–Letnikov.

Let us consider the calculation of images with the Caputo derivative. In the first step, we demonstrate that the calculation of the Caputo derivative on an infinite interval images makes it possible to express the fractional derivative of the function g(t). In the second step, we analyze the calculation of the Caputo derivative on a truncated interval and the initial condition problem arising at t = t0. Thus, we demonstrate ...

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Publisher Resources

ISBN: 9781786302694Purchase Link