$Mild solutions for semilinear fractional differential equations$

Mild solutions for semilinear fractional differential equations

This paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the $alpha$-norm. We prove existence and uniqueness, assuming that the linear part generates an analytic compact bounded semigroup, and the nonlinear part is a...

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Bibliographic Details
Main Authors:	Gisele M. Mophou, Gaston M. N'Guerekata
Format:	Article
Language:	English
Published:	Texas State University 2009-01-01
Series:	Electronic Journal of Differential Equations
Subjects:	Fractional differential equation
Online Access:	http://ejde.math.txstate.edu/Volumes/2009/21/abstr.html

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spelling	doaj-b017e78b8dd4493b90a4100161f065922020-11-24T23:09:09ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-01-01200921,19Mild solutions for semilinear fractional differential equationsGisele M. MophouGaston M. N'GuerekataThis paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the $alpha$-norm. We prove existence and uniqueness, assuming that the linear part generates an analytic compact bounded semigroup, and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.http://ejde.math.txstate.edu/Volumes/2009/21/abstr.htmlFractional differential equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Gisele M. Mophou Gaston M. N'Guerekata
spellingShingle	Gisele M. Mophou Gaston M. N'Guerekata Mild solutions for semilinear fractional differential equations Electronic Journal of Differential Equations Fractional differential equation
author_facet	Gisele M. Mophou Gaston M. N'Guerekata
author_sort	Gisele M. Mophou
title	Mild solutions for semilinear fractional differential equations
title_short	Mild solutions for semilinear fractional differential equations
title_full	Mild solutions for semilinear fractional differential equations
title_fullStr	Mild solutions for semilinear fractional differential equations
title_full_unstemmed	Mild solutions for semilinear fractional differential equations
title_sort	mild solutions for semilinear fractional differential equations
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2009-01-01
description	This paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the $alpha$-norm. We prove existence and uniqueness, assuming that the linear part generates an analytic compact bounded semigroup, and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.
topic	Fractional differential equation
url	http://ejde.math.txstate.edu/Volumes/2009/21/abstr.html
work_keys_str_mv	AT giselemmophou mildsolutionsforsemilinearfractionaldifferentialequations AT gastonmnguerekata mildsolutionsforsemilinearfractionaldifferentialequations
_version_	1725611215694069760

Mild solutions for semilinear fractional differential equations

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