izvuzmathИзвестия высших учебных заведений. МатематикаIzvestiya Vysshikh Uchebnykh Zavedenii. Matematika0021-34462076-4626Казанский (Приволжский) федеральный университет10.26907/0021-3446-2024-9-45-55izvuzmath-111Research ArticleСтатьиСУЩЕСТВОВАНИЕ АСИМПТОТИЧЕСКИ ПОЧТИ ПЕРИОДИЧЕСКОГО РЕШЕНИЯ ДРОБНОЙ ПОЛУЛИНЕЙНОЙ ЗАДАЧИExistence of an asymptotically almost periodic solution for a fractional semilinear problemМагхсудиС.MaghsoodiS.

Сохейла Магхсуди

Бабольсар

Soheyla Maghsoodi

Babolsar

smaghsoodi@stu.umz.ac.irНеаматиА.NeamatyA.

Абдолали Неамати

Бабольсар

Abdolali Neamaty

Babolsar

namaty@umz.ac.irУниверситет МазандаранаИранMazandaran UniversityIslamic Republic of Iran202425092024094555Copyright © Магхсуди С., Неамати А., 20242024Магхсуди С., Неамати А.Maghsoodi S., Neamaty A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://izvuzmath.elpub.ru/jour/article/view/111

В данной статье рассматривается дробная полулинейная задача в секвенциально компактном банаховом пространстве $X$: $x^{\alpha}(t) = A(t)x(t) + f(t, x(t))$, $t \in \mathbb{R}^{+}$, с начальным условием $x(0) = x_{0}$, $x_{0} \in X$. Здесь $A$ является генератором эволюционной системы $({U(t,s)})_{t \leq s \leq 0}$, а $f$ --заданная функция, удовлетворяющая некоторым условиям. Мы исследуем, имеет ли это дробное полулинейное интегро-дифференциальное уравнение асимптотически почти периодическое решение.

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.

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The authors declare that there are no conflicts of interest present.