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Relative Controllability of Caputo Fractional‐Order Stochastic Delay System Driven by Lévy Noise.

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Title: Relative Controllability of Caputo Fractional‐Order Stochastic Delay System Driven by Lévy Noise.
Authors: Zhong, Yun1 (AUTHOR), Li, Mengmeng1,2 (AUTHOR) mmli@gzu.edu.cn, Wu, Huaiqin (AUTHOR) huaiqinwu@ysu.edu.cn
Source: Journal of Applied Mathematics. 5/9/2026, Vol. 2026, p1-17. 17p.
Subjects: Controllability in systems engineering, Caputo fractional derivatives, Random noise theory, Schwarz inequality, Matrix functions, Fixed point theory, Matrices (Mathematics)
Abstract: In this paper, we study the relative controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS by using the delayed Mittag–Leffler matrix function. Then, using Grammian matrix, we discuss the relative controllability of linear FSDS. In addition, the relative controllability of nonlinear FSDS is discussed using the Cauchy–Schwarz inequality, Jensen's inequality, Ito∧'s formula, and Krasnoselskii fixed‐point theorem. Finally, an example is given to verify the theoretical results. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Relative Controllability of Caputo Fractional‐Order Stochastic Delay System Driven by Lévy Noise.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 5/9/2026, Vol. 2026, p1-17. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Controllability+in+systems+engineering%22">Controllability in systems engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Random+noise+theory%22">Random noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Schwarz+inequality%22">Schwarz inequality</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink>
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  Label: Abstract
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  Data: In this paper, we study the relative controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS by using the delayed Mittag–Leffler matrix function. Then, using Grammian matrix, we discuss the relative controllability of linear FSDS. In addition, the relative controllability of nonlinear FSDS is discussed using the Cauchy–Schwarz inequality, Jensen's inequality, Ito∧'s formula, and Krasnoselskii fixed‐point theorem. Finally, an example is given to verify the theoretical results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1155/jama/6812601
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 17
        StartPage: 1
    Subjects:
      – SubjectFull: Controllability in systems engineering
        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
      – SubjectFull: Random noise theory
        Type: general
      – SubjectFull: Schwarz inequality
        Type: general
      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Fixed point theory
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
    Titles:
      – TitleFull: Relative Controllability of Caputo Fractional‐Order Stochastic Delay System Driven by Lévy Noise.
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            NameFull: Zhong, Yun
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            NameFull: Li, Mengmeng
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            NameFull: Wu, Huaiqin
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          Dates:
            – D: 09
              M: 05
              Text: 5/9/2026
              Type: published
              Y: 2026
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              Value: 2026
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            – TitleFull: Journal of Applied Mathematics
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