Explicit solutions and finite-time stability for fractional delay systems

Ahmed M. Elshenhab; Xing Tao Wang; Mohamed Hosny

doi:10.1016/j.amc.2025.129388

Explicit solutions and finite-time stability for fractional delay systems

Ahmed M. Elshenhab^*, Xing Tao Wang, Mohamed Hosny

^*Corresponding author for this work

Interdisciplinary Research Center for Finance and Digital Economy

Research output: Contribution to journal › Article › peer-review

Abstract

Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.

Original language	English
Article number	129388
Journal	Applied Mathematics and Computation
Volume	498
DOIs	https://doi.org/10.1016/j.amc.2025.129388
State	Published - 1 Aug 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier Inc.

Keywords

Explicit solutions
Finite-time stability
Fractional delay systems
Fractional delayed matrix Mittag-Leffler function

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2025.129388

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title = "Explicit solutions and finite-time stability for fractional delay systems",

abstract = "Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.",

keywords = "Explicit solutions, Finite-time stability, Fractional delay systems, Fractional delayed matrix Mittag-Leffler function",

author = "Elshenhab, \{Ahmed M.\} and Wang, \{Xing Tao\} and Mohamed Hosny",

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year = "2025",

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doi = "10.1016/j.amc.2025.129388",

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T1 - Explicit solutions and finite-time stability for fractional delay systems

AU - Elshenhab, Ahmed M.

AU - Wang, Xing Tao

AU - Hosny, Mohamed

PY - 2025/8/1

Y1 - 2025/8/1

N2 - Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.

AB - Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.

KW - Explicit solutions

KW - Finite-time stability

KW - Fractional delay systems

KW - Fractional delayed matrix Mittag-Leffler function

UR - https://www.scopus.com/pages/publications/85218866495

U2 - 10.1016/j.amc.2025.129388

DO - 10.1016/j.amc.2025.129388

M3 - Article

AN - SCOPUS:85218866495

SN - 0096-3003

VL - 498

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 129388

ER -

Explicit solutions and finite-time stability for fractional delay systems

Abstract

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Keywords

ASJC Scopus subject areas

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