Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference

Coşkun Yakar; Dilara Karslıoğlu

doi:10.33401/fujma.1785134

Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference

Abstract

In this study, we explore the connection between unperturbed matrix differential systems that exhibit variations in both their initial conditions and the starting time. Through the application of variation of parameters methods, we construct integral representations that reveal this relationship. To formulate Lipschitz-type stability criteria under the presence of an initial time shift in nonlinear differential systems, it is essential to employ the variational framework derived from the unperturbed matrix model.

Keywords

Supporting Institution

This research received no external funding.

Ethical Statement

This article does not contain any studies with human or animal subjects. It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.

Thanks

The author would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Coşkun Yakar
0000-0002-7759-7939
Türkiye

Dilara Karslıoğlu ^*
0000-0001-7141-7346
Türkiye

Publication Date

September 30, 2026

Submission Date

September 16, 2025

Acceptance Date

September 28, 2026

Published in Issue

Year 2026 Volume: 9 Number: 3

DOI

https://doi.org/10.33401/fujma.1785134

IZ

https://izlik.org/JA56YN24LB

Cite

RIS / Bibtex

APA

Yakar, C., & Karslıoğlu, D. (2026). Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference. Fundamental Journal of Mathematics and Applications, 9(3), 179-194. https://doi.org/10.33401/fujma.1785134

AMA

1.Yakar C, Karslıoğlu D. Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference. Fundam. J. Math. Appl. 2026;9(3):179-194. doi:10.33401/fujma.1785134

Chicago

Yakar, Coşkun, and Dilara Karslıoğlu. 2026. “Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems With Initial Time Difference”. Fundamental Journal of Mathematics and Applications 9 (3): 179-94. https://doi.org/10.33401/fujma.1785134.

EndNote

Yakar C, Karslıoğlu D (September 1, 2026) Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference. Fundamental Journal of Mathematics and Applications 9 3 179–194.

IEEE

[1]C. Yakar and D. Karslıoğlu, “Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference”, Fundam. J. Math. Appl., vol. 9, no. 3, pp. 179–194, Sept. 2026, doi: 10.33401/fujma.1785134.

ISNAD

Yakar, Coşkun - Karslıoğlu, Dilara. “Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems With Initial Time Difference”. Fundamental Journal of Mathematics and Applications 9/3 (September 1, 2026): 179-194. https://doi.org/10.33401/fujma.1785134.

JAMA

1.Yakar C, Karslıoğlu D. Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference. Fundam. J. Math. Appl. 2026;9:179–194.

MLA

Yakar, Coşkun, and Dilara Karslıoğlu. “Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems With Initial Time Difference”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 3, Sept. 2026, pp. 179-94, doi:10.33401/fujma.1785134.

Vancouver

1.Coşkun Yakar, Dilara Karslıoğlu. Variation of Parameters Representations and Lipschitz-Type Stability for Unperturbed Matrix Differential Systems with Initial Time Difference. Fundam. J. Math. Appl. 2026 Sep. 1;9(3):179-94. doi:10.33401/fujma.1785134