Analytic solutions of a generalized complex multi-dimensional system with fractional order
The Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. We demonstrate that in specific functional domains, the suggested system produces a global solution. Conver...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-01-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0029 |
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| _version_ | 1832570423930257408 |
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| author | Baleanu Dumitru Ibrahim Rabha W. |
| author_facet | Baleanu Dumitru Ibrahim Rabha W. |
| author_sort | Baleanu Dumitru |
| collection | DOAJ |
| description | The Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. We demonstrate that in specific functional domains, the suggested system produces a global solution. Convergence toward the stable point is investigated. Some special cases are illustrated including the rotated Koebe function, which is used for creating the optimal solutions, where these functions are convex univalent in the open unit disk. |
| format | Article |
| id | doaj-art-4b25e055a2f44a6fa2ebc9fb5f357b7b |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-4b25e055a2f44a6fa2ebc9fb5f357b7b2025-02-02T15:45:16ZengDe GruyterDemonstratio Mathematica2391-46612025-01-0158117919210.1515/dema-2024-0029Analytic solutions of a generalized complex multi-dimensional system with fractional orderBaleanu Dumitru0Ibrahim Rabha W.1Institute of Space Sciences, R76900 Magurele-Bucharest, RomaniaInformation and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, Nasiriyah, 64001, IraqThe Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. We demonstrate that in specific functional domains, the suggested system produces a global solution. Convergence toward the stable point is investigated. Some special cases are illustrated including the rotated Koebe function, which is used for creating the optimal solutions, where these functions are convex univalent in the open unit disk.https://doi.org/10.1515/dema-2024-0029fractional differential equationsfractional differential operatork-symbol calculusfractional calculusanalytic functionsthe cauchy-schwartz inequality30c4530c55 |
| spellingShingle | Baleanu Dumitru Ibrahim Rabha W. Analytic solutions of a generalized complex multi-dimensional system with fractional order Demonstratio Mathematica fractional differential equations fractional differential operator k-symbol calculus fractional calculus analytic functions the cauchy-schwartz inequality 30c45 30c55 |
| title | Analytic solutions of a generalized complex multi-dimensional system with fractional order |
| title_full | Analytic solutions of a generalized complex multi-dimensional system with fractional order |
| title_fullStr | Analytic solutions of a generalized complex multi-dimensional system with fractional order |
| title_full_unstemmed | Analytic solutions of a generalized complex multi-dimensional system with fractional order |
| title_short | Analytic solutions of a generalized complex multi-dimensional system with fractional order |
| title_sort | analytic solutions of a generalized complex multi dimensional system with fractional order |
| topic | fractional differential equations fractional differential operator k-symbol calculus fractional calculus analytic functions the cauchy-schwartz inequality 30c45 30c55 |
| url | https://doi.org/10.1515/dema-2024-0029 |
| work_keys_str_mv | AT baleanudumitru analyticsolutionsofageneralizedcomplexmultidimensionalsystemwithfractionalorder AT ibrahimrabhaw analyticsolutionsofageneralizedcomplexmultidimensionalsystemwithfractionalorder |