Basic Theory of Impulsive Quaternion-Valued Linear Systems

Ardak Kashkynbayev; Manat Mustafa

doi:10.1007/978-3-030-69292-6_21

Basic Theory of Impulsive Quaternion-Valued Linear Systems

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

Abstract

In this chapter, we consider linear quaternion-valued ordinary differential equations (QDEs) with impulses at fixed times. We consider linear homogeneous and nonhomogeneous impulsive QDEs. Further, we prove the analogue of the Floquet theorem for linear periodic QDEs and discuss some consequences. Moreover, we prove the existence of bounded solutions to nonhomogeneous impulsive QDEs. Finally, we study periodic solutions of nonhomogeneous impulsive QDEs.

Original language	English
Title of host publication	Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018
Editors	Allaberen Ashyralyev, Tynysbek Sh. Kalmenov, Michael V. Ruzhansky, Michael V. Ruzhansky, Makhmud A. Sadybekov, Durvudkhan Suragan
Publisher	Springer, Cham
Pages	273-287
Number of pages	15
Volume	351
ISBN (Electronic)	978-3-030-69292-6
ISBN (Print)	978-3-030-69291-9
DOIs	https://doi.org/10.1007/978-3-030-69292-6_21
Publication status	Published - 2021

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	351
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Funding

Acknowledgements AK was supported by Nazarbayev University Faculty Development Competitive Research Grants N 090118FD5353. MM was supported by Nazarbayev University Faculty Development Competitive Research Grants N 090118FD5342.

Funders	Funder number
Nazarbayev University	090118FD5342, 090118FD5353

Keywords

Floquet theory
Impulsive differential equations
Periodic solutions
Quaternions
Stability

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-030-69292-6_21

Cite this

Kashkynbayev, A., & Mustafa, M. (2021). Basic Theory of Impulsive Quaternion-Valued Linear Systems. In A. Ashyralyev, T. S. Kalmenov, M. V. Ruzhansky, M. V. Ruzhansky, M. A. Sadybekov, & D. Suragan (Eds.), Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018 (Vol. 351, pp. 273-287). (Springer Proceedings in Mathematics and Statistics; Vol. 351). Springer, Cham. https://doi.org/10.1007/978-3-030-69292-6_21

Basic Theory of Impulsive Quaternion-Valued Linear Systems. / Kashkynbayev, Ardak ; Mustafa, Manat.
Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018. ed. / Allaberen Ashyralyev; Tynysbek Sh. Kalmenov; Michael V. Ruzhansky; Michael V. Ruzhansky; Makhmud A. Sadybekov; Durvudkhan Suragan. Vol. 351 Springer, Cham, 2021. p. 273-287 (Springer Proceedings in Mathematics and Statistics; Vol. 351).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kashkynbayev, A & Mustafa, M 2021, Basic Theory of Impulsive Quaternion-Valued Linear Systems. in A Ashyralyev, TS Kalmenov, MV Ruzhansky, MV Ruzhansky, MA Sadybekov & D Suragan (eds), Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018. vol. 351, Springer Proceedings in Mathematics and Statistics, vol. 351, Springer, Cham, pp. 273-287. https://doi.org/10.1007/978-3-030-69292-6_21

Kashkynbayev A , Mustafa M. Basic Theory of Impulsive Quaternion-Valued Linear Systems. In Ashyralyev A, Kalmenov TS, Ruzhansky MV, Ruzhansky MV, Sadybekov MA, Suragan D, editors, Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018. Vol. 351. Springer, Cham. 2021. p. 273-287. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-69292-6_21

Kashkynbayev, Ardak ; Mustafa, Manat. / Basic Theory of Impulsive Quaternion-Valued Linear Systems. Functional Analysis in Interdisciplinary Applications—II - ICAAM, 2018. editor / Allaberen Ashyralyev ; Tynysbek Sh. Kalmenov ; Michael V. Ruzhansky ; Michael V. Ruzhansky ; Makhmud A. Sadybekov ; Durvudkhan Suragan. Vol. 351 Springer, Cham, 2021. pp. 273-287 (Springer Proceedings in Mathematics and Statistics).

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Basic Theory of Impulsive Quaternion-Valued Linear Systems

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