Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale
The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Control and Optimization |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720723001492 |
| _version_ | 1827316346453491712 |
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| author | Nada K. Mahdi Ayad R. Khudair |
| author_facet | Nada K. Mahdi Ayad R. Khudair |
| author_sort | Nada K. Mahdi |
| collection | DOAJ |
| description | The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical inequality are to the solutions of the exact FDEs. Meanwhile, the generalized HUS result is obtained as a direct corollary. To achieve this goal, we solve the aforementioned equations utilizing the time scale version of the Laplace transform. Subsequently, the HUS is investigated in accordance with theseăsolutions. |
| first_indexed | 2024-04-24T23:12:59Z |
| format | Article |
| id | doaj.art-bf6242035cb642d382e13d9a0dcfa893 |
| institution | Directory Open Access Journal |
| issn | 2666-7207 |
| language | English |
| last_indexed | 2024-04-24T23:12:59Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj.art-bf6242035cb642d382e13d9a0dcfa8932024-03-17T07:58:54ZengElsevierResults in Control and Optimization2666-72072024-03-0114100347Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scaleNada K. Mahdi0Ayad R. Khudair1Department of Mathematics, Basrah University, IraqDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq; Corresponding author.The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical inequality are to the solutions of the exact FDEs. Meanwhile, the generalized HUS result is obtained as a direct corollary. To achieve this goal, we solve the aforementioned equations utilizing the time scale version of the Laplace transform. Subsequently, the HUS is investigated in accordance with theseăsolutions.http://www.sciencedirect.com/science/article/pii/S2666720723001492Time scaleTime scale Laplace transformLinear dynamic equationsFractional calculusUlam StabilityFractional dynamic equations |
| spellingShingle | Nada K. Mahdi Ayad R. Khudair Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale Results in Control and Optimization Time scale Time scale Laplace transform Linear dynamic equations Fractional calculus Ulam Stability Fractional dynamic equations |
| title | Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale |
| title_full | Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale |
| title_fullStr | Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale |
| title_full_unstemmed | Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale |
| title_short | Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale |
| title_sort | linear fractional dynamic equations hyers ulam stability analysis on time scale |
| topic | Time scale Time scale Laplace transform Linear dynamic equations Fractional calculus Ulam Stability Fractional dynamic equations |
| url | http://www.sciencedirect.com/science/article/pii/S2666720723001492 |
| work_keys_str_mv | AT nadakmahdi linearfractionaldynamicequationshyersulamstabilityanalysisontimescale AT ayadrkhudair linearfractionaldynamicequationshyersulamstabilityanalysisontimescale |