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Controllability analysis of a class of (1,2)‐Caputo time‐fractional systems.

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Title: Controllability analysis of a class of (1,2)‐Caputo time‐fractional systems.
Authors: Aadi, Asmaa1 (AUTHOR), Tajani, Asmae2 (AUTHOR) tajaniasmae@ua.pt, El Alaoui, Fatima Zahrae1 (AUTHOR)
Source: Asian Journal of Control. Mar2026, Vol. 28 Issue 2, p526-539. 14p.
Subjects: Controllability in systems engineering, Caputo fractional derivatives, Optimal control theory, Digital computer simulation, Fractional calculus, Cosine function
Abstract: The main purpose of this paper is to examine the controllability of linear time‐fractional systems involving the Caputo fractional derivative of order 1<γ<2$$ 1<\gamma <2 $$. We first define the concept of controllability and then develop a theoretical framework to demonstrate certain exact and approximate controllability properties of time‐fractional systems. This is achieved using a novel expression for the controllability operator based on the formulation of the mild solution of our problem, fractional calculus theory, and the cosine family. Subsequently, we extend the Hilbert uniqueness method (HUM) approach to determine the optimal control of our problem. Finally, we present numerical simulations for one‐dimensional systems with different types of actuators, either zonal or pointwise, to support the theoretical results discussed in the paper. These simulations achieve a satisfactory error margin, which determines the effectiveness of our method. [ABSTRACT FROM AUTHOR]
Copyright of Asian Journal of Control 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: The main purpose of this paper is to examine the controllability of linear time‐fractional systems involving the Caputo fractional derivative of order 1&lt;γ&lt;2$$ 1&lt;\gamma &lt;2 $$. We first define the concept of controllability and then develop a theoretical framework to demonstrate certain exact and approximate controllability properties of time‐fractional systems. This is achieved using a novel expression for the controllability operator based on the formulation of the mild solution of our problem, fractional calculus theory, and the cosine family. Subsequently, we extend the Hilbert uniqueness method (HUM) approach to determine the optimal control of our problem. Finally, we present numerical simulations for one‐dimensional systems with different types of actuators, either zonal or pointwise, to support the theoretical results discussed in the paper. These simulations achieve a satisfactory error margin, which determines the effectiveness of our method. [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder&#39;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.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1002/asjc.3636
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        Text: English
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        PageCount: 14
        StartPage: 526
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        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Digital computer simulation
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      – SubjectFull: Fractional calculus
        Type: general
      – SubjectFull: Cosine function
        Type: general
    Titles:
      – TitleFull: Controllability analysis of a class of (1,2)‐Caputo time‐fractional systems.
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            NameFull: Aadi, Asmaa
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            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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