Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions
In this paper a regularization scheme for a family of uncertain fuzzy systems of differential equations with respect to the uncertain parameters is introduced. Important fundamental properties of the solutions are discussed on the basis of the established technique and new results are proposed. More...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023195?viewType=HTML |
| _version_ | 1827823175671480320 |
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| author | Anatoliy Martynyuk Gani Stamov Ivanka Stamova Yulya Martynyuk–Chernienko |
| author_facet | Anatoliy Martynyuk Gani Stamov Ivanka Stamova Yulya Martynyuk–Chernienko |
| author_sort | Anatoliy Martynyuk |
| collection | DOAJ |
| description | In this paper a regularization scheme for a family of uncertain fuzzy systems of differential equations with respect to the uncertain parameters is introduced. Important fundamental properties of the solutions are discussed on the basis of the established technique and new results are proposed. More precisely, existence and uniqueness criteria of solutions of the regularized equations are established. In addition, an estimation is proposed for the distance between two solutions. Our results contribute to the progress in the area of the theory of fuzzy systems of differential equations and extend the existing results to the uncertain case. The proposed results also open the horizon for generalizations including equations with delays and some modifications of the Lyapunov theory. In addition, the opportunities for applications of such results to the design of efficient fuzzy controllers are numerous. |
| first_indexed | 2024-03-12T02:07:24Z |
| format | Article |
| id | doaj.art-a1f120edadaf4b99945f6f6ec21ea857 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-12T02:07:24Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-a1f120edadaf4b99945f6f6ec21ea8572023-09-07T01:59:58ZengAIMS PressElectronic Research Archive2688-15942023-05-013173832384710.3934/era.2023195Regularization scheme for uncertain fuzzy differential equations: Analysis of solutionsAnatoliy Martynyuk0Gani Stamov1Ivanka Stamova2Yulya Martynyuk–Chernienko31. S. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov str., Kiev-57, 03057, Ukraine2. Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA2. Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA1. S. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov str., Kiev-57, 03057, UkraineIn this paper a regularization scheme for a family of uncertain fuzzy systems of differential equations with respect to the uncertain parameters is introduced. Important fundamental properties of the solutions are discussed on the basis of the established technique and new results are proposed. More precisely, existence and uniqueness criteria of solutions of the regularized equations are established. In addition, an estimation is proposed for the distance between two solutions. Our results contribute to the progress in the area of the theory of fuzzy systems of differential equations and extend the existing results to the uncertain case. The proposed results also open the horizon for generalizations including equations with delays and some modifications of the Lyapunov theory. In addition, the opportunities for applications of such results to the design of efficient fuzzy controllers are numerous.https://www.aimspress.com/article/doi/10.3934/era.2023195?viewType=HTMLfuzzy differential equationsregularizationuncertain parametersanalysis |
| spellingShingle | Anatoliy Martynyuk Gani Stamov Ivanka Stamova Yulya Martynyuk–Chernienko Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions Electronic Research Archive fuzzy differential equations regularization uncertain parameters analysis |
| title | Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions |
| title_full | Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions |
| title_fullStr | Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions |
| title_full_unstemmed | Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions |
| title_short | Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions |
| title_sort | regularization scheme for uncertain fuzzy differential equations analysis of solutions |
| topic | fuzzy differential equations regularization uncertain parameters analysis |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023195?viewType=HTML |
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