Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems
In this paper, we study the existence and uniqueness of solutions for nabla fractional systems. By using the properties of bijective functions, we obtain a necessary and sufficient condition ensuring the existence and uniqueness of solutions for a class of fractional discrete systems. Furthermore, w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/12/723 |
| _version_ | 1827639235137503232 |
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| author | Jikai Yang Hongli Li Long Zhang |
| author_facet | Jikai Yang Hongli Li Long Zhang |
| author_sort | Jikai Yang |
| collection | DOAJ |
| description | In this paper, we study the existence and uniqueness of solutions for nabla fractional systems. By using the properties of bijective functions, we obtain a necessary and sufficient condition ensuring the existence and uniqueness of solutions for a class of fractional discrete systems. Furthermore, we derive two sufficient conditions guaranteeing the existence of solutions by means of a nonlinear functional analysis method. In addition, the above conclusions are extended to high-dimensional delayed systems. Finally, two examples are given to illustrate the validity of our results. |
| first_indexed | 2024-03-09T16:35:44Z |
| format | Article |
| id | doaj.art-e750ebc737eb45889d1021f5a5f1d625 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:35:44Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e750ebc737eb45889d1021f5a5f1d6252023-11-24T14:57:34ZengMDPI AGFractal and Fractional2504-31102022-12-0161272310.3390/fractalfract6120723Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional SystemsJikai Yang0Hongli Li1Long Zhang2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaIn this paper, we study the existence and uniqueness of solutions for nabla fractional systems. By using the properties of bijective functions, we obtain a necessary and sufficient condition ensuring the existence and uniqueness of solutions for a class of fractional discrete systems. Furthermore, we derive two sufficient conditions guaranteeing the existence of solutions by means of a nonlinear functional analysis method. In addition, the above conclusions are extended to high-dimensional delayed systems. Finally, two examples are given to illustrate the validity of our results.https://www.mdpi.com/2504-3110/6/12/723nabla fractional systemsinvertible functionproof by contradictionexistence and uniqueness |
| spellingShingle | Jikai Yang Hongli Li Long Zhang Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems Fractal and Fractional nabla fractional systems invertible function proof by contradiction existence and uniqueness |
| title | Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems |
| title_full | Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems |
| title_fullStr | Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems |
| title_full_unstemmed | Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems |
| title_short | Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems |
| title_sort | necessary and sufficient conditions for existence and uniqueness of solutions to nabla fractional systems |
| topic | nabla fractional systems invertible function proof by contradiction existence and uniqueness |
| url | https://www.mdpi.com/2504-3110/6/12/723 |
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