Research Article

Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems

Number: 56 September 30, 2026

Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems

Abstract

In this paper, a class of multi-delayed Mittag--Leffler (ML) type matrix functions is developed, and the Laplace transform is employed to derive explicit analytical representations of the solutions to the corresponding initial value problems (IVPs) for Hilfer fractional linear systems with several delays and nonpermutable coefficient matrices. In addition, the Ulam--Hyers (UH) stability of the proposed fractional multi-delayed model is established. Several nontrivial numerical examples are presented to illustrate the theoretical findings.

Keywords

Mittag-Leffler type matrix function, representation of solution, Laplace transform, stability

References

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APA
Aydın, M. (2026). Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems. Journal of New Theory, 56, 1-22. https://doi.org/10.53570/jnt.1937582
AMA
1.Aydın M. Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems. JNT. 2026;(56):1-22. doi:10.53570/jnt.1937582
Chicago
Aydın, Mustafa. 2026. “Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems”. Journal of New Theory, nos. 56: 1-22. https://doi.org/10.53570/jnt.1937582.
EndNote
Aydın M (September 1, 2026) Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems. Journal of New Theory 56 1–22.
IEEE
[1]M. Aydın, “Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems”, JNT, no. 56, pp. 1–22, Sept. 2026, doi: 10.53570/jnt.1937582.
ISNAD
Aydın, Mustafa. “Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems”. Journal of New Theory. 56 (September 1, 2026): 1-22. https://doi.org/10.53570/jnt.1937582.
JAMA
1.Aydın M. Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems. JNT. 2026;:1–22.
MLA
Aydın, Mustafa. “Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems”. Journal of New Theory, no. 56, Sept. 2026, pp. 1-22, doi:10.53570/jnt.1937582.
Vancouver
1.Mustafa Aydın. Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems. JNT. 2026 Sep. 1;(56):1-22. doi:10.53570/jnt.1937582