Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales
In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary va...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1804 |
| _version_ | 1797482044827107328 |
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| author | Ahmed A. El-Deeb Dumitru Baleanu Jan Awrejcewicz |
| author_facet | Ahmed A. El-Deeb Dumitru Baleanu Jan Awrejcewicz |
| author_sort | Ahmed A. El-Deeb |
| collection | DOAJ |
| description | In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation. |
| first_indexed | 2024-03-09T22:23:40Z |
| format | Article |
| id | doaj.art-f89841490b8244e2aa704b64b79f15aa |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:23:40Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f89841490b8244e2aa704b64b79f15aa2023-11-23T19:11:12ZengMDPI AGSymmetry2073-89942022-08-01149180410.3390/sym14091804Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time ScalesAhmed A. El-Deeb0Dumitru Baleanu1Jan Awrejcewicz2Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, EgyptInstitute of Space Science, 077125 Magurele, RomaniaDepartment of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, PolandIn this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation.https://www.mdpi.com/2073-8994/14/9/1804Gronwall’s inequalitydynamic inequalitytime scalesLeibniz integral rule on time scales |
| spellingShingle | Ahmed A. El-Deeb Dumitru Baleanu Jan Awrejcewicz Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales Symmetry Gronwall’s inequality dynamic inequality time scales Leibniz integral rule on time scales |
| title | Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales |
| title_full | Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales |
| title_fullStr | Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales |
| title_full_unstemmed | Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales |
| title_short | Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities and Their Applications on Time Scales |
| title_sort | δ gronwall bellman pachpatte dynamic inequalities and their applications on time scales |
| topic | Gronwall’s inequality dynamic inequality time scales Leibniz integral rule on time scales |
| url | https://www.mdpi.com/2073-8994/14/9/1804 |
| work_keys_str_mv | AT ahmedaeldeeb dgronwallbellmanpachpattedynamicinequalitiesandtheirapplicationsontimescales AT dumitrubaleanu dgronwallbellmanpachpattedynamicinequalitiesandtheirapplicationsontimescales AT janawrejcewicz dgronwallbellmanpachpattedynamicinequalitiesandtheirapplicationsontimescales |