Skip to Main Content
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

4Fractional Modeling of the Diffusive Interface

4.1. Introduction

Many physical and chemical processes, such as heat transfer in materials [BAT 01], eddy currents in electrical machines [RET 99], electrochemistry in batteries [SAB 06] and so on, are governed by diffusive partial derivative equations.

Practically, we are mainly concerned by the modeling of the diffusive interface at the boundary of the considered process, such as the voltage/current relationship in an accumulator [LIN 00] or the temperature/heat flux for heat transfer [BEN 06].

It has been demonstrated long ago [OLD 74] that the diffusive interface is characterized by a fractional order behavior in the frequency domain with n = 0.5. It is for this reason that a great number of research works have been devoted to the fractional modeling of diffusive interfaces, using various fractional order models [COI 01, LIN 01a]. Some of these models are motivated by physical properties [BAT 02], but many others are only identification (or black box) models motivated by the efficiency of the approximation.

Therefore, in this chapter, our purpose is to investigate why fractional models are adapted to the modeling of diffusive interfaces, and whether any fractional model can provide a correct physical response to this problem [MAA 15].

In order to formulate an objective response, we use a prototype interface, i.e. heat transfer in a plane wall.

Two families of fractional models are investigated: commensurate order models, ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Analysis, Modeling and Stability of Fractional Order Differential Systems 2

Analysis, Modeling and Stability of Fractional Order Differential Systems 2

Jean-Claude Trigeassou, Nezha Maamri

Publisher Resources

ISBN: 9781786302694Purchase Link