Stochastic controllability for a non-autonomous fractional neutral differential equation with infinite delay in abstract space
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917613723975680 |
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| author | Khatoon, Areefa Raheem, Abdur Afreen, Asma |
| author_facet | Khatoon, Areefa Raheem, Abdur Afreen, Asma |
| contents | This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and stochastic analysis techniques have been implemented to achieve the main result. We prove the existence of mild solution and controllability of the system by using the theory of measure of non-compactness, fixed point theorems, and $k$-set contractive mapping. An example is given to demonstrate the effectiveness of the abstract result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic controllability for a non-autonomous fractional neutral differential equation with infinite delay in abstract space Khatoon, Areefa Raheem, Abdur Afreen, Asma Optimization and Control 26A33, 93B05, 34K05, 34K35, 47H08 This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and stochastic analysis techniques have been implemented to achieve the main result. We prove the existence of mild solution and controllability of the system by using the theory of measure of non-compactness, fixed point theorems, and $k$-set contractive mapping. An example is given to demonstrate the effectiveness of the abstract result. |
| title | Stochastic controllability for a non-autonomous fractional neutral differential equation with infinite delay in abstract space |
| topic | Optimization and Control 26A33, 93B05, 34K05, 34K35, 47H08 |
| url | https://arxiv.org/abs/2403.08825 |