A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales
As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have their own unique features wh...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/4/450 |
| _version_ | 1797538064947478528 |
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| author | Chao Wang Ravi P. Agarwal |
| author_facet | Chao Wang Ravi P. Agarwal |
| author_sort | Chao Wang |
| collection | DOAJ |
| description | As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have their own unique features which the difference and differential equations do not possess and these advantages have been highlighted in describing some complicated dynamical behavior in the hybrid time process. In this review article, we conduct a survey of abstract analysis and applied dynamic equations on hybrid time scales, some recent main results and the related developments on hybrid time scales will be reported and the future research related to this research field is discussed. The results presented in this article can be extended and generalized to study both pure mathematical analysis and real applications such as mathematical physics, biological dynamical models and neural networks, etc. |
| first_indexed | 2024-03-10T12:25:10Z |
| format | Article |
| id | doaj.art-7eafcd1025454aa3a1c701ff29fc4458 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T12:25:10Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-7eafcd1025454aa3a1c701ff29fc44582023-11-21T15:04:50ZengMDPI AGEntropy1099-43002021-04-0123445010.3390/e23040450A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time ScalesChao Wang0Ravi P. Agarwal1Department of Mathematics, Yunnan University, Kunming 650091, ChinaDepartment of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USAAs an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have their own unique features which the difference and differential equations do not possess and these advantages have been highlighted in describing some complicated dynamical behavior in the hybrid time process. In this review article, we conduct a survey of abstract analysis and applied dynamic equations on hybrid time scales, some recent main results and the related developments on hybrid time scales will be reported and the future research related to this research field is discussed. The results presented in this article can be extended and generalized to study both pure mathematical analysis and real applications such as mathematical physics, biological dynamical models and neural networks, etc.https://www.mdpi.com/1099-4300/23/4/450dynamic equationstime scalesgeneral theory |
| spellingShingle | Chao Wang Ravi P. Agarwal A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales Entropy dynamic equations time scales general theory |
| title | A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales |
| title_full | A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales |
| title_fullStr | A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales |
| title_full_unstemmed | A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales |
| title_short | A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales |
| title_sort | survey of function analysis and applied dynamic equations on hybrid time scales |
| topic | dynamic equations time scales general theory |
| url | https://www.mdpi.com/1099-4300/23/4/450 |
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