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On asymptotic periodic solutions of fractional differential equations and applications.
- Source :
-
Proceedings of the American Mathematical Society . Dec2023, Vol. 151 Issue 12, p5299-5312. 14p. - Publication Year :
- 2023
-
Abstract
- 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 \le 1, (*) 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 \mathbb {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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFERENTIAL forms
*BANACH spaces
*COPPER
*FRACTIONAL differential equations
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 172751227
- Full Text :
- https://doi.org/10.1090/proc/16484