On the Cauchy problem for the Langevin-type fractional equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911533088374784 |
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| author | Fayziev, Yusuf Jumaeva, Shakhnoza |
| author_facet | Fayziev, Yusuf Jumaeva, Shakhnoza |
| contents | In this article, the Cauchy problem for the Langevin-type time-fractional equation $D_t^β(D_t^αu(t))+D_t^β(Au(t))=f(t),(0<t\leq T)$ is studied. Here $α,β\in(0,1)$, $D_t^α, D_t^β$ is the Caputo derivative and $A$ is an unbounded self-adjoint operator in a separable Hilbert space. Under certain conditions, we establish the existence and uniqueness of the solution and provide an explicit representation of it using eigenfunction expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Cauchy problem for the Langevin-type fractional equation Fayziev, Yusuf Jumaeva, Shakhnoza Analysis of PDEs 35R11 In this article, the Cauchy problem for the Langevin-type time-fractional equation $D_t^β(D_t^αu(t))+D_t^β(Au(t))=f(t),(0<t\leq T)$ is studied. Here $α,β\in(0,1)$, $D_t^α, D_t^β$ is the Caputo derivative and $A$ is an unbounded self-adjoint operator in a separable Hilbert space. Under certain conditions, we establish the existence and uniqueness of the solution and provide an explicit representation of it using eigenfunction expansions. |
| title | On the Cauchy problem for the Langevin-type fractional equation |
| topic | Analysis of PDEs 35R11 |
| url | https://arxiv.org/abs/2505.08252 |