A Linearized Stability Theorem for Nonlinear Delay Fractional Differential Equations Article Swipe
Hoang The Tuan
,
Hieu Trinh
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1109/tac.2018.2791485
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1109/tac.2018.2791485
In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional differential equation with a time delay is asymptotically stable if its linearization at the equilibrium is asymptotically stable. Our approach based on a technique which converts the linear part of the equation into a diagonal one. Then using properties of generalized Mittag-Leffler functions, the construction of an associated Lyapunov--Perron operator and the Banach contraction mapping theorem, we obtain the desired result.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/tac.2018.2791485
- OA Status
- green
- Cited By
- 49
- References
- 21
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2625846854
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- OpenAlex ID
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https://openalex.org/W2625846854Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1109/tac.2018.2791485Digital Object Identifier
- Title
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A Linearized Stability Theorem for Nonlinear Delay Fractional Differential EquationsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2018Year of publication
- Publication date
-
2018-01-09Full publication date if available
- Authors
-
Hoang The Tuan, Hieu TrinhList of authors in order
- Landing page
-
https://doi.org/10.1109/tac.2018.2791485Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1706.03936Direct OA link when available
- Concepts
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Mathematics, Linearization, Nonlinear system, Stability theory, Mathematical analysis, Contraction mapping, Differential equation, Banach space, Lyapunov function, Exponential stability, Applied mathematics, Fixed-point theorem, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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49Total citation count in OpenAlex
- Citations by year (recent)
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2025: 5, 2024: 4, 2023: 8, 2022: 8, 2021: 4Per-year citation counts (last 5 years)
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21Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.technique | 69 |
| abstract_inverted_index.associated | 93 |
| abstract_inverted_index.asymptotic | 9 |
| abstract_inverted_index.fractional | 12, 45 |
| abstract_inverted_index.functions, | 88 |
| abstract_inverted_index.linearized | 8 |
| abstract_inverted_index.precisely, | 20 |
| abstract_inverted_index.properties | 84 |
| abstract_inverted_index.(Lyapunov's | 33 |
| abstract_inverted_index.contraction | 99 |
| abstract_inverted_index.equilibrium | 40, 60 |
| abstract_inverted_index.generalized | 86 |
| abstract_inverted_index.construction | 90 |
| abstract_inverted_index.differential | 13, 46 |
| abstract_inverted_index.linearization | 25, 57 |
| abstract_inverted_index.Mittag-Leffler | 87 |
| abstract_inverted_index.asymptotically | 53, 62 |
| abstract_inverted_index.Lyapunov--Perron | 94 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 94 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.92170757 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |