Representation of a solution for a fractional linear system with pure delay

Chengbin Liang; Jin Rong Wang; D. O'Regan

doi:10.1016/j.aml.2017.09.015

Representation of a solution for a fractional linear system with pure delay

Chengbin Liang
, Jin Rong Wang
, D. O'Regan

Mathematics

Guizhou University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

51 Citations (Scopus)

Abstract

This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.

Original language	English
Pages (from-to)	72-78
Number of pages	7
Journal	Applied Mathematics Letters
Volume	77
DOIs	https://doi.org/10.1016/j.aml.2017.09.015
Publication status	Published - Mar 2018

Keywords

Finite time stability
Fractional delayed matrices cosine and sine
Fractional linear system with pure delay
Representation of solution

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10.1016/j.aml.2017.09.015

Cite this

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abstract = "This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.",

keywords = "Finite time stability, Fractional delayed matrices cosine and sine, Fractional linear system with pure delay, Representation of solution",

author = "Chengbin Liang and Wang, \{Jin Rong\} and D. O'Regan",

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AU - Liang, Chengbin

AU - Wang, Jin Rong

AU - O'Regan, D.

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N2 - This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.

AB - This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.

KW - Finite time stability

KW - Fractional delayed matrices cosine and sine

KW - Fractional linear system with pure delay

KW - Representation of solution

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DO - 10.1016/j.aml.2017.09.015

M3 - Article

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VL - 77

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EP - 78

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Representation of a solution for a fractional linear system with pure delay

Abstract

Keywords

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