Publication result detail

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.; BIOLEK, Z.

Original Title

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

English Title

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

Type

WoS Article

Original Abstract

In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of s(& alpha;)-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag-Leffler function E-& alpha;(,& beta;), & beta; = & alpha;. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for & alpha; = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny's function of type & epsilon;(k) (t, c; & alpha;, & alpha;), where c and k are the corresponding pole and its multiplicity, respectively.

English abstract

In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of s(& alpha;)-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag-Leffler function E-& alpha;(,& beta;), & beta; = & alpha;. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for & alpha; = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny's function of type & epsilon;(k) (t, c; & alpha;, & alpha;), where c and k are the corresponding pole and its multiplicity, respectively.

Keywords

Mittag-Leffler function; commensurate fractional-order system; basis function; impulse response

Key words in English

Mittag-Leffler function; commensurate fractional-order system; basis function; impulse response

Authors

BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.; BIOLEK, Z.

RIV year

2024

Released

13.07.2023

Publisher

MDPI

Location

BASEL

ISBN

1999-4893

Periodical

Algorithms

Volume

16

Number

7

State

Swiss Confederation

Pages from

1

Pages to

22

Pages count

22

URL

https://www.mdpi.com/1999-4893/16/7/335

Full text in the Digital Library

http://hdl.handle.net/11012/244995

BibTex

@article{BUT184376,
  author="Dalibor {Biolek} and Viera {Biolková} and Zdeněk {Kolka} and Zdeněk {Biolek}",
  title="Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems",
  journal="Algorithms",
  year="2023",
  volume="16",
  number="7",
  pages="1--22",
  doi="10.3390/a16070335",
  url="https://www.mdpi.com/1999-4893/16/7/335"
}

Documents

algorithms-16-00335-v3