Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects
We apply known special functions from the literature (and these include the Fox <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">H</mi><mo>–</m...
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| author | Safoura Rezaei Aderyani Reza Saadati Donal O’Regan Fehaid Salem Alshammari |
| author_facet | Safoura Rezaei Aderyani Reza Saadati Donal O’Regan Fehaid Salem Alshammari |
| author_sort | Safoura Rezaei Aderyani |
| collection | DOAJ |
| description | We apply known special functions from the literature (and these include the Fox <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">H</mi><mo>–</mo></mrow></semantics></math></inline-formula>function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">G</mi><mo>–</mo></mrow></semantics></math></inline-formula>function, the Fox–Wright function and the Meijer <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">G</mi><mo>–</mo></mrow></semantics></math></inline-formula>function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory. |
| first_indexed | 2024-04-24T18:03:10Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:03:10Z |
| publishDate | 2024-03-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e6552e1d715941ca9cd8645c0f2f791c2024-03-27T13:53:16ZengMDPI AGMathematics2227-73902024-03-0112690410.3390/math12060904Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical AspectsSafoura Rezaei Aderyani0Reza Saadati1Donal O’Regan2Fehaid Salem Alshammari3School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, IranSchool of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, IrelandDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi ArabiaWe apply known special functions from the literature (and these include the Fox <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">H</mi><mo>–</mo></mrow></semantics></math></inline-formula>function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">G</mi><mo>–</mo></mrow></semantics></math></inline-formula>function, the Fox–Wright function and the Meijer <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">G</mi><mo>–</mo></mrow></semantics></math></inline-formula>function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory.https://www.mdpi.com/2227-7390/12/6/904stability resultsspecial aggregate mapsnumerical method |
| spellingShingle | Safoura Rezaei Aderyani Reza Saadati Donal O’Regan Fehaid Salem Alshammari Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects Mathematics stability results special aggregate maps numerical method |
| title | Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects |
| title_full | Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects |
| title_fullStr | Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects |
| title_full_unstemmed | Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects |
| title_short | Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects |
| title_sort | uncertain asymptotic stability analysis of a fractional order system with numerical aspects |
| topic | stability results special aggregate maps numerical method |
| url | https://www.mdpi.com/2227-7390/12/6/904 |
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