A General Version of Carathéodory's Existence and Uniqueness Theorem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916768892583936 |
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| author | de Carvalho-Neto, Paulo M. Frota, Cícero L. Torelli, Pedro G. P. |
| author_facet | de Carvalho-Neto, Paulo M. Frota, Cícero L. Torelli, Pedro G. P. |
| contents | In this paper, we establish a general version of Carathéodory's existence and uniqueness theorem for a semilinear system of integro-differential equations arising from differential equations with distinct orders of Caputo fractional derivative. The main result of our work demonstrates that the integrability order of the Carathéodory function $f$ must be at least greater than the maximum of the reciprocals of all differentiation orders in the system; otherwise, even the existence of a solution cannot be guaranteed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Version of Carathéodory's Existence and Uniqueness Theorem de Carvalho-Neto, Paulo M. Frota, Cícero L. Torelli, Pedro G. P. Classical Analysis and ODEs Functional Analysis 26A33, 34A08, 34A12 In this paper, we establish a general version of Carathéodory's existence and uniqueness theorem for a semilinear system of integro-differential equations arising from differential equations with distinct orders of Caputo fractional derivative. The main result of our work demonstrates that the integrability order of the Carathéodory function $f$ must be at least greater than the maximum of the reciprocals of all differentiation orders in the system; otherwise, even the existence of a solution cannot be guaranteed. |
| title | A General Version of Carathéodory's Existence and Uniqueness Theorem |
| topic | Classical Analysis and ODEs Functional Analysis 26A33, 34A08, 34A12 |
| url | https://arxiv.org/abs/2505.24516 |