Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative
The primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ψ-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and analytic. The findings are based on the application of the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1050 |
| _version_ | 1797598263391551488 |
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| author | Sonuc Zorlu Adham Gudaimat |
| author_facet | Sonuc Zorlu Adham Gudaimat |
| author_sort | Sonuc Zorlu |
| collection | DOAJ |
| description | The primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ψ-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and analytic. The findings are based on the application of the theory of fractional calculus, semigroup theory, and the fixed-point method, mainly Schauder’s fixed-point theorem. In addition, we assume that the corresponding linear system is approximately controllable. An example is provided to illustrate the obtained theoretical results. |
| first_indexed | 2024-03-11T03:16:56Z |
| format | Article |
| id | doaj.art-e044d67946dd42ec9f9393930ded69bc |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:56Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e044d67946dd42ec9f9393930ded69bc2023-11-18T03:30:14ZengMDPI AGSymmetry2073-89942023-05-01155105010.3390/sym15051050Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo DerivativeSonuc Zorlu0Adham Gudaimat1Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus, Mersin 10, TurkeyDepartment of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus, Mersin 10, TurkeyThe primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ψ-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and analytic. The findings are based on the application of the theory of fractional calculus, semigroup theory, and the fixed-point method, mainly Schauder’s fixed-point theorem. In addition, we assume that the corresponding linear system is approximately controllable. An example is provided to illustrate the obtained theoretical results.https://www.mdpi.com/2073-8994/15/5/1050approximate controllabilityfractional differential equationscompact operatorssemigroup theorySchauder’s fixed-point theorem |
| spellingShingle | Sonuc Zorlu Adham Gudaimat Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative Symmetry approximate controllability fractional differential equations compact operators semigroup theory Schauder’s fixed-point theorem |
| title | Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative |
| title_full | Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative |
| title_fullStr | Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative |
| title_full_unstemmed | Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative |
| title_short | Approximate Controllability of Fractional Evolution Equations with <i>ψ</i>-Caputo Derivative |
| title_sort | approximate controllability of fractional evolution equations with i ψ i caputo derivative |
| topic | approximate controllability fractional differential equations compact operators semigroup theory Schauder’s fixed-point theorem |
| url | https://www.mdpi.com/2073-8994/15/5/1050 |
| work_keys_str_mv | AT sonuczorlu approximatecontrollabilityoffractionalevolutionequationswithipsicaputoderivative AT adhamgudaimat approximatecontrollabilityoffractionalevolutionequationswithipsicaputoderivative |