Existence of an asymptotically almost periodic solution for a fractional semilinear problem
https://doi.org/10.26907/0021-3446-2024-9-45-55
Abstract
In this research, we consider the fractional semilinear problem in a sequentially compact Banach space $X$: $x^{\alpha}(t)=A(t)x(t)+f(t,x(t))$, $t\in \mathbb R^{+} $, with the initial condition $x(0)=x_{0}$, $ x_{0} \in X $, where $A$ is the generator of an evolution system $({U(t,s)})_{t\leq s \leq {0}}$ and $f$ is a given function satisfying some assumptions. We study this fractional semilinear integro-differential equation and examine when it has an asymptotically almost periodic solution.
About the Authors
S. Maghsoodi
Mazandaran University
Islamic Republic of Iran
Islamic Republic of Iran
Soheyla Maghsoodi
Babolsar
A. Neamaty
Mazandaran University
Islamic Republic of Iran
Islamic Republic of Iran
Abdolali Neamaty
Babolsar
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Review
For citations:
Maghsoodi S., Neamaty A. Existence of an asymptotically almost periodic solution for a fractional semilinear problem. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(9):45-55. (In Russ.) https://doi.org/10.26907/0021-3446-2024-9-45-55
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