Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system D0,tμ,νzt+Azt+Ωzt−h=ft of order 1<μ<2 and type 0...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2661343 |
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| author | Nazim I. Mahmudov |
| author_facet | Nazim I. Mahmudov |
| author_sort | Nazim I. Mahmudov |
| collection | DOAJ |
| description | We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system D0,tμ,νzt+Azt+Ωzt−h=ft of order 1<μ<2 and type 0≤ν≤1, with nonpermutable matrices A and Ω. Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear time-delay systems with permutable matrices and new even for these fractional delay systems. |
| format | Article |
| id | doaj-art-a38f9c31f80040bbbbe8564a46a3910c |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a38f9c31f80040bbbbe8564a46a3910c2025-08-20T03:38:18ZengWileyJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/2661343Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers StabilityNazim I. Mahmudov0Department of MathematicsWe introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system D0,tμ,νzt+Azt+Ωzt−h=ft of order 1<μ<2 and type 0≤ν≤1, with nonpermutable matrices A and Ω. Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear time-delay systems with permutable matrices and new even for these fractional delay systems.http://dx.doi.org/10.1155/2022/2661343 |
| spellingShingle | Nazim I. Mahmudov Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability Journal of Applied Mathematics |
| title | Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability |
| title_full | Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability |
| title_fullStr | Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability |
| title_full_unstemmed | Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability |
| title_short | Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability |
| title_sort | analytical solution of the fractional linear time delay systems and their ulam hyers stability |
| url | http://dx.doi.org/10.1155/2022/2661343 |
| work_keys_str_mv | AT nazimimahmudov analyticalsolutionofthefractionallineartimedelaysystemsandtheirulamhyersstability |