Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations
This paper investigates Ulam stability of delay fractional difference equations. First, a useful equality of double fractional sums is employed and discrete Gronwall’s inequality of delay type is provided. A delay discrete-time Mittag-Leffler function is used and its non-negativity condition is giv...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2025-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://gc.vgtu.lt/index.php/MMA/article/view/20017 |
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| author | Shu-Yu Yang Guo-Cheng Wu |
| author_facet | Shu-Yu Yang Guo-Cheng Wu |
| author_sort | Shu-Yu Yang |
| collection | DOAJ |
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This paper investigates Ulam stability of delay fractional difference equations. First, a useful equality of double fractional sums is employed and discrete Gronwall’s inequality of delay type is provided. A delay discrete-time Mittag-Leffler function is used and its non-negativity condition is given. With the solutions’ existences, Ulam stability condition is presented to discuss the error estimation of exact and approximate solutions.
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| format | Article |
| id | doaj-art-ac40e31885844525a3685773423ce8da |
| institution | Kabale University |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-ac40e31885844525a3685773423ce8da2025-01-27T16:30:19ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-01-0130110.3846/mma.2025.20017Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equationsShu-Yu Yang0Guo-Cheng Wu1School of Mathematical Sciences, Bohai University, 120000 Jinzhou, ChinaKey Laboratory of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, 400065 Chongqing, China This paper investigates Ulam stability of delay fractional difference equations. First, a useful equality of double fractional sums is employed and discrete Gronwall’s inequality of delay type is provided. A delay discrete-time Mittag-Leffler function is used and its non-negativity condition is given. With the solutions’ existences, Ulam stability condition is presented to discuss the error estimation of exact and approximate solutions. https://gc.vgtu.lt/index.php/MMA/article/view/20017delay fractional difference equationsdiscrete Gronwall’s inequalityuniqueness of solutionUlam stability |
| spellingShingle | Shu-Yu Yang Guo-Cheng Wu Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations Mathematical Modelling and Analysis delay fractional difference equations discrete Gronwall’s inequality uniqueness of solution Ulam stability |
| title | Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations |
| title_full | Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations |
| title_fullStr | Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations |
| title_full_unstemmed | Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations |
| title_short | Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations |
| title_sort | discrete gronwall s inequality for ulam stability of delay fractional difference equations |
| topic | delay fractional difference equations discrete Gronwall’s inequality uniqueness of solution Ulam stability |
| url | https://gc.vgtu.lt/index.php/MMA/article/view/20017 |
| work_keys_str_mv | AT shuyuyang discretegronwallsinequalityforulamstabilityofdelayfractionaldifferenceequations AT guochengwu discretegronwallsinequalityforulamstabilityofdelayfractionaldifferenceequations |