On asymptotic periodic solutions of fractional differential equations and applications
| Autor: | Luong, Vu Trong, Huy, Nguyen Duc, Van Minh, Nguyen, Vien, Nguyen Ngoc |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the Caputo's sense, $A$ is a linear operator in a Banach space $\X$ that may be unbounded and $f$ satisfies the property that $\lim_{t\to \infty} (f(t+1)-f(t))=0$ which we will call asymptotic $1$-periodicity. By using the spectral theory of functions on the half line we derive analogs of Katznelson-Tzafriri and Massera Theorems. Namely, we give sufficient conditions in terms of spectral properties of the operator $A$ for all asymptotic mild solutions of Eq. (*) to be asymptotic $1$-periodic, or there exists an asymptotic mild solution that is asymptotic $1$-periodic. Comment: 13 pages. arXiv admin note: text overlap with arXiv:1910.08609 |
| Databáze: | arXiv |
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