Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space
In the current work, we deal with a class of stochastic time-fractional integral equations in Hilbert space by studying their well-posedness and regularity. Precisely, we use the celebrity fixed point theorem to prove the well-posedness of the problem by imposing the global Lipschitz and the linear...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2022-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2022.2119587 |
| _version_ | 1798002883093856256 |
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| author | Zineb Arab Cemil Tunç |
| author_facet | Zineb Arab Cemil Tunç |
| author_sort | Zineb Arab |
| collection | DOAJ |
| description | In the current work, we deal with a class of stochastic time-fractional integral equations in Hilbert space by studying their well-posedness and regularity. Precisely, we use the celebrity fixed point theorem to prove the well-posedness of the problem by imposing the global Lipschitz and the linear growth conditions. Further, we prove the spatial and temporal regularity by imposing only a regularity condition on the initial value. An important example is considered in order to confirm and support the validity of our theoretical results. |
| first_indexed | 2024-04-11T11:59:16Z |
| format | Article |
| id | doaj.art-1555c360ef554dfa86905c45e49a4291 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-11T11:59:16Z |
| publishDate | 2022-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-1555c360ef554dfa86905c45e49a42912022-12-22T04:24:57ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552022-12-0116178879810.1080/16583655.2022.2119587Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert spaceZineb Arab0Cemil Tunç1Department of Chemistry, Faculty of Material sciences, Batna 1 University, Batna, AlgeriaDepartment of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, TurkeyIn the current work, we deal with a class of stochastic time-fractional integral equations in Hilbert space by studying their well-posedness and regularity. Precisely, we use the celebrity fixed point theorem to prove the well-posedness of the problem by imposing the global Lipschitz and the linear growth conditions. Further, we prove the spatial and temporal regularity by imposing only a regularity condition on the initial value. An important example is considered in order to confirm and support the validity of our theoretical results.https://www.tandfonline.com/doi/10.1080/16583655.2022.2119587Integral equationsRiemann–Liouville integral operatorcylindrical Wiener processfixed point theoremspatial regularitytemporal regularity |
| spellingShingle | Zineb Arab Cemil Tunç Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space Journal of Taibah University for Science Integral equations Riemann–Liouville integral operator cylindrical Wiener process fixed point theorem spatial regularity temporal regularity |
| title | Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space |
| title_full | Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space |
| title_fullStr | Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space |
| title_full_unstemmed | Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space |
| title_short | Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space |
| title_sort | well posedness and regularity of some stochastic time fractional integral equations in hilbert space |
| topic | Integral equations Riemann–Liouville integral operator cylindrical Wiener process fixed point theorem spatial regularity temporal regularity |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2022.2119587 |
| work_keys_str_mv | AT zinebarab wellposednessandregularityofsomestochastictimefractionalintegralequationsinhilbertspace AT cemiltunc wellposednessandregularityofsomestochastictimefractionalintegralequationsinhilbertspace |