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

References

  1. J. Diblík, D. Y. Khusainov, Representation of solutions of discrete delayed system $x(k+1)=Ax(k)+Bx(k-m)+f(k)$ with commutative matrices, Journal of Mathematical Analysis and Applications 318 (1) (2006) 63–76.
  2. M. Li, J. Wang, Finite time stability of fractional delay differential equations}, Applied Mathematics Letters 64 (2017) 170–176.
  3. N. I. Mahmudov, Delayed perturbation of Mittag-Leffler functions and their applications to fractional linear delay differential equations, Mathematical Methods in the Applied Sciences 42 (16) (2019) 5489–5497.
  4. N. I. Mahmudov, Analytical solution of the fractional linear time-delay systems and their Ulam-Hyers stability, Journal of Applied Mathematics 2022 (1) (2022) 2661343.
  5. X. Zhang, M. Li, Existence and Ulam-type stability for fractional multi-delay differential systems, Fractal and Fractional 9 (5) (2025) 288.
  6. L.-W. Li, Y.-F. Lu, F.-X. Wang, X.-G. Liu, Mittag-Leffler stability and synchronization of multi-delayed fractional neural networks via Halanay inequality, Circuits, Systems, and Signal Processing 44 (2) (2025) 862–887.
  7. M. Aydin, Controllability of nonlinear fractional systems with multiple state and control delays, Journal of Nonlinear Modeling and Analysis 7 (5) (2025) 1965–1981.
  8. A. M. Elshenhab, G. AlNemer, X. Wang, Exact solutions to multiple-delayed linear discrete matrix equations, Symmetry 17 (10) (2025) 1684.

Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Mathematical Methods and Special Functions

Journal Section

Research Article

Publication Date

September 30, 2026

Submission Date

April 25, 2026

Acceptance Date

July 8, 2026

Published in Issue

Year 2026 Number: 56

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

 

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