Recursive-operational method for fractional systems: System theory without Laplace transform

Gabriel Bengochea; Manuel Ortigueira; Luis Verde-Star; António Mendes Lopes

doi:10.1515/9783110571929-005

Recursive-operational method for fractional systems: System theory without Laplace transform

Gabriel Bengochea, Manuel Ortigueira, Luis Verde-Star, António Mendes Lopes

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.

Original language	English
Title of host publication	Applications in Engineering, Life and Social Sciences, Part B
Publisher	De Gruyter
Pages	119-147
Number of pages	29
ISBN (Electronic)	9783110571929
ISBN (Print)	9783110570922
DOIs	https://doi.org/10.1515/9783110571929-005
Publication status	Published - 1 Jan 2019

Keywords

Fractional derivative
Fractional systems
Operational calculus

Access to Document

10.1515/9783110571929-005

Cite this

@inbook{f5379fb41ea34804a86d16773be70b9a,

title = "Recursive-operational method for fractional systems: System theory without Laplace transform",

abstract = "In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.",

keywords = "Fractional derivative, Fractional systems, Operational calculus",

author = "Gabriel Bengochea and Manuel Ortigueira and Luis Verde-Star and Lopes, {Ant{\'o}nio Mendes}",

year = "2019",

month = jan,

day = "1",

doi = "10.1515/9783110571929-005",

language = "English",

isbn = "9783110570922",

pages = "119--147",

booktitle = "Applications in Engineering, Life and Social Sciences, Part B",

publisher = "De Gruyter",

address = "Germany",

}

TY - CHAP

T1 - Recursive-operational method for fractional systems: System theory without Laplace transform

AU - Bengochea, Gabriel

AU - Ortigueira, Manuel

AU - Verde-Star, Luis

AU - Lopes, António Mendes

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.

AB - In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.

KW - Fractional derivative

KW - Fractional systems

KW - Operational calculus

UR - http://www.scopus.com/inward/record.url?scp=85096737928&partnerID=8YFLogxK

U2 - 10.1515/9783110571929-005

DO - 10.1515/9783110571929-005

M3 - Chapter

AN - SCOPUS:85096737928

SN - 9783110570922

SP - 119

EP - 147

BT - Applications in Engineering, Life and Social Sciences, Part B

PB - De Gruyter

ER -

Recursive-operational method for fractional systems: System theory without Laplace transform

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this