An explicit solution of linear conformable systems with variable coefficients

Mustafa Aydın

An explicit solution of linear conformable systems with variable coefficients

Abstract

This paper is mainly devoted to exact solutions to the initial value problem for linear conformable systems with variable coefficients. The famous method known as the generalized Peano-Baker series, which inholds the conformable integral, is exploited to acquire the state-transition matrix. A representation of an exact solution in a closed interval for linear confromable systems with variable coefficients is determined with the help of this matrix. It is verified by showing that the determined exact solution satisfies the systems step by step. Moreover, another exact solution in the same closed interval is identified thanks to the method of variation of parameters. The existence and uniqueness of the second exact solution to the systems are provided by the Banach contraction mapping principle. This provides that the representations of the two solutions coincide although they are obtained by completely different approaches and they have completely different structures. A couple of examples are presented to exmplify the use of the findings.

Keywords

References

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Details

Primary Language

English

Subjects

Clinical Chemistry

Journal Section

Research Article

Authors

Mustafa Aydın ^*
0000-0003-0132-9636
Türkiye

Publication Date

December 9, 2024

Submission Date

September 26, 2023

Acceptance Date

December 4, 2023

Published in Issue

Year 2024 Volume: 42 Number: 6

IZ

https://izlik.org/JA33NP29DD

Cite

RIS / Bibtex

APA

Aydın, M. (2024). An explicit solution of linear conformable systems with variable coefficients. Sigma Journal of Engineering and Natural Sciences, 42(6), 1806-1812. https://izlik.org/JA33NP29DD

AMA

1.Aydın M. An explicit solution of linear conformable systems with variable coefficients. SIGMA. 2024;42(6):1806-1812. https://izlik.org/JA33NP29DD

Chicago

Aydın, Mustafa. 2024. “An Explicit Solution of Linear Conformable Systems With Variable Coefficients”. Sigma Journal of Engineering and Natural Sciences 42 (6): 1806-12. https://izlik.org/JA33NP29DD.

EndNote

Aydın M (December 1, 2024) An explicit solution of linear conformable systems with variable coefficients. Sigma Journal of Engineering and Natural Sciences 42 6 1806–1812.

IEEE

[1]M. Aydın, “An explicit solution of linear conformable systems with variable coefficients”, SIGMA, vol. 42, no. 6, pp. 1806–1812, Dec. 2024, [Online]. Available: https://izlik.org/JA33NP29DD

ISNAD

Aydın, Mustafa. “An Explicit Solution of Linear Conformable Systems With Variable Coefficients”. Sigma Journal of Engineering and Natural Sciences 42/6 (December 1, 2024): 1806-1812. https://izlik.org/JA33NP29DD.

JAMA

1.Aydın M. An explicit solution of linear conformable systems with variable coefficients. SIGMA. 2024;42:1806–1812.

MLA

Aydın, Mustafa. “An Explicit Solution of Linear Conformable Systems With Variable Coefficients”. Sigma Journal of Engineering and Natural Sciences, vol. 42, no. 6, Dec. 2024, pp. 1806-12, https://izlik.org/JA33NP29DD.

Vancouver

1.Mustafa Aydın. An explicit solution of linear conformable systems with variable coefficients. SIGMA [Internet]. 2024 Dec. 1;42(6):1806-12. Available from: https://izlik.org/JA33NP29DD