| dc.contributor.author | Hujing Tan | |
| dc.contributor.author | Pu Wang | |
| dc.contributor.other | Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China | |
| dc.contributor.other | School of Mathematics and Statistics, Henan University, Kaifeng 475004, China | |
| dc.date.accessioned | 2025-08-27T02:32:32Z | |
| dc.date.accessioned | 2025-10-08T08:07:07Z | |
| dc.date.available | 2025-10-08T08:07:07Z | |
| dc.date.issued | 2025-07 | |
| dc.identifier.uri | https://www.aimspress.com/article/doi/10.3934/math.2025745 | |
| dc.identifier.uri | http://digilib.fisipol.ugm.ac.id/repo/handle/15717717/35623 | |
| dc.description.abstract | This paper investigates the well-posedness of mild solutions for a linear time-fractional Cable equation on a bounded domain $ \Omega \subset \mathbb{R}^d $ ($ d \geq 1 $) with a $ C^2 $ boundary: \begin{document}$ \begin{align*} \left\{ \begin{aligned} &\partial_t u = \partial_t^{1-\alpha}\Delta u - \partial_t^{1-\beta}u + f, \quad (t, x) \in (0, T) \times \Omega, \\ &u(0, x) = u_0(x), \quad x\in \Omega, \\ &u = 0, \quad x\in\partial\Omega, \end{aligned} \right. \end{align*} $\end{document} where $ 0 < \alpha $, $ \beta < 1 $, and $ \partial_{t}^{1-\beta} $ and $ \partial_{t}^{1-\alpha} $ denote the Riemann–Liouville fractional derivatives of orders $ 1-\beta $ and $ 1-\alpha $, respectively. By employing the eigenfunction expansion method, we constructed the mild solution and established its definition. Utilizing the Banach contraction mapping principle and properties of the Mittag-Leffler function, we derived the existence, uniqueness, and regularity of mild solutions for the linear problem. Furthermore, we introduced a weighted Hölder continuous function space and demonstrated the existence and uniqueness of mild solutions within this frameworks. The results obtained in this work contribute to the theoretical understanding of time-fractional Cable equations and serve as a foundation for further studies in fractional-order diffusion processes. | |
| dc.language.iso | EN | |
| dc.publisher | AIMS Press | |
| dc.subject.lcc | Mathematics | |
| dc.title | The well-posedness and regularity of mild solutions to the time-fractional Cable equation | |
| dc.type | Article | |
| dc.description.keywords | time-fractional cable equation | |
| dc.description.keywords | well-posedness | |
| dc.description.keywords | weighted hölder space | |
| dc.description.pages | 16624-16641 | |
| dc.description.doi | 10.3934/math.2025745 | |
| dc.title.journal | AIMS Mathematics | |
| dc.identifier.e-issn | 2473-6988 | |
| dc.identifier.oai | b5e51ca88fdc42d99a039c1f578c4bb9 | |
| dc.journal.info | Volume 10, Issue 7 | |
