Fractional relaxation equations on Banach spaces
type: Item
instance of: scholarly article
title: Fractional relaxation equations on Banach spaces
zbMATH Open document ID: 1214.34047
author: Carlos Lizama
author: H. Prado
published in: Applied Mathematics Letters
publication date: 2010-10-25T00:00:00Z
review text: The authors study the abstract fractional relaxation equation \[ u^{\prime}(t)-AD_t^{\alpha}u(t)+u(t)=f(t), \quad 0<\alpha < 1,\quad t \geq 0, \quad u(0)=0, \] on a complex Banach space \(X\), where \(A\) is a closed linear operator, \(D_t^{\alpha}\) is the Caputo derivative of fractional order \(\alpha \in (0,1)\), and \(f\) is an \(X\)-valued function. They obtain some results on existence and qualitative properties of solutions and also study conditions under which the solution operator has the properties of maximal regularity and \(L^p\) integrability. They characterize these properties in the Hilbert space case.
reviewed by: S. G. Samko
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5804494
zbMATH Keywords: fractional evolution equations
zbMATH Keywords: derivatives of fractional order
zbMATH Keywords: regularized resolvents
MaRDI profile type: Publication
full work available at URL: j.aml.2009.08.019
OpenAlex ID: W2035705583
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DOI: 10.1016/J.AML.2009.08.019
description: scientific article; zbMATH DE number 5804494