\(S\)-asymptotically \(\omega \)-periodic solutions of semilinear fractional integro-differential equations
type: Item
instance of: scholarly article
title: \(S\)-asymptotically \(\omega \)-periodic solutions of semilinear fractional integro-differential equations
zbMATH Open document ID: 1176.47035
author: Claudio Cuevas
author: Julio César De Souza
published in: Applied Mathematics Letters
publication date: 2009-06-10T00:00:00Z
review text: The authors consider the following semilinear fractional integro-differential equation \[ v'(t) = \int_0^t \frac{(t - s)^{\alpha - 2}}{\Gamma (\alpha - 1)} Av(s)\,ds + f(t,v(t)), \quad t \geq 0, \quad v(0) = u_0 \in X, \] where \(1 < \alpha < 2\), \(A:D(A) \subset X \to X\) is a linear densely defined operator of sectorial type on a complex Banach space \(X\), and \(f:[0,\infty )\times X \to X\) is a continuous function satisfying a suitable Lipschitz type condition. The existence and uniqueness of an \(S\)-asymptotically \(\omega\)-periodic mild solution to this problem is obtained.
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 5563910
zbMATH Keywords: \(S\)-asymptotically \(\omega\)-periodic function
zbMATH Keywords: solution operator
zbMATH Keywords: fractional integral
zbMATH Keywords: semilinear integro-differential equations
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: j.aml.2008.07.013
OpenAlex ID: W2072349082
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DOI: 10.1016/J.AML.2008.07.013
description: scientific article; zbMATH DE number 5563910