Geodesic
Existence of an asymptotically almost periodic solution for a fractional semilinear problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 45-55 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: asymptotically almost periodic solution, semilinear fractional problem, evolution system. 
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S. Maghsoodi; A. Neamaty. Existence of an asymptotically almost periodic solution for a fractional semilinear problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 45-55. http://geodesic.mathdoc.fr/item/IVM_2024_9_a4/

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