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Article

Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays

by
Tingting Xie
and
Mengmeng Li
*
Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(12), 1129; https://doi.org/10.3390/axioms12121129
Submission received: 9 November 2023 / Revised: 11 December 2023 / Accepted: 12 December 2023 / Published: 15 December 2023
(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization)
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Abstract

This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results.
Keywords: fractional delay differential equations; impulsive delayed Mittag–Leffler-type vector function; finite-time stability fractional delay differential equations; impulsive delayed Mittag–Leffler-type vector function; finite-time stability

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MDPI and ACS Style

Xie, T.; Li, M. Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays. Axioms 2023, 12, 1129. https://doi.org/10.3390/axioms12121129

AMA Style

Xie T, Li M. Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays. Axioms. 2023; 12(12):1129. https://doi.org/10.3390/axioms12121129

Chicago/Turabian Style

Xie, Tingting, and Mengmeng Li. 2023. "Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays" Axioms 12, no. 12: 1129. https://doi.org/10.3390/axioms12121129

APA Style

Xie, T., & Li, M. (2023). Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays. Axioms, 12(12), 1129. https://doi.org/10.3390/axioms12121129

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