Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918160621371392 |
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| author | Brahim, Hamza Ben Alaoui, Fatima-Zahrae El Tajani, Asmae Torres, Delfim F. M. |
| author_facet | Brahim, Hamza Ben Alaoui, Fatima-Zahrae El Tajani, Asmae Torres, Delfim F. M. |
| contents | We prove the existence and uniqueness of mild solutions for a specific class of time-fractional $ψ$-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution. This expression is formulated as an integral, incorporating Mainardi's Wright-type function. Furthermore, we provide various valuable properties associated with the operators present in the mild solution. Additionally, employing the fixed-point technique and Grönwall's inequality, we establish the existence and uniqueness of the mild solution. To illustrate our results, we conclude with an example of a time-fractional equation, presenting the expression for its corresponding mild solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01754 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two Brahim, Hamza Ben Alaoui, Fatima-Zahrae El Tajani, Asmae Torres, Delfim F. M. Analysis of PDEs Functional Analysis Spectral Theory 35A01, 35R11, 46B50 We prove the existence and uniqueness of mild solutions for a specific class of time-fractional $ψ$-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution. This expression is formulated as an integral, incorporating Mainardi's Wright-type function. Furthermore, we provide various valuable properties associated with the operators present in the mild solution. Additionally, employing the fixed-point technique and Grönwall's inequality, we establish the existence and uniqueness of the mild solution. To illustrate our results, we conclude with an example of a time-fractional equation, presenting the expression for its corresponding mild solution. |
| title | Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two |
| topic | Analysis of PDEs Functional Analysis Spectral Theory 35A01, 35R11, 46B50 |
| url | https://arxiv.org/abs/2402.01754 |