On the existence of mild solutions to some semilinear fractional integro-differential equations

On the existence of mild solutions to some semilinear fractional integro-differential equations

This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear...

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Main Authors: Toka Diagana, G. M. Mophou, Gaston N'Guerekata
Format: Article
Language:English
Published: University of Szeged 2010-09-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=518
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spelling doaj-70106897dab2434c8d2938020f527c732021-07-14T07:21:22ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752010-09-0120105811710.14232/ejqtde.2010.1.58518On the existence of mild solutions to some semilinear fractional integro-differential equationsToka Diagana0G. M. Mophou1Gaston N'Guerekata2Howard University, Washington, DC, U.S.A.Universite des Antilles et de La Guyane, Campus Fouillole, GuadeloupeMorgan State University, E. Cold Spring Lane, Baltimore, MD, U.S.A.This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for $t > 0$ and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=518
collection DOAJ
language English
format Article
sources DOAJ
author Toka Diagana
G. M. Mophou
Gaston N'Guerekata
spellingShingle Toka Diagana
G. M. Mophou
Gaston N'Guerekata
On the existence of mild solutions to some semilinear fractional integro-differential equations
Electronic Journal of Qualitative Theory of Differential Equations
author_facet Toka Diagana
G. M. Mophou
Gaston N'Guerekata
author_sort Toka Diagana
title On the existence of mild solutions to some semilinear fractional integro-differential equations
title_short On the existence of mild solutions to some semilinear fractional integro-differential equations
title_full On the existence of mild solutions to some semilinear fractional integro-differential equations
title_fullStr On the existence of mild solutions to some semilinear fractional integro-differential equations
title_full_unstemmed On the existence of mild solutions to some semilinear fractional integro-differential equations
title_sort on the existence of mild solutions to some semilinear fractional integro-differential equations
publisher University of Szeged
series Electronic Journal of Qualitative Theory of Differential Equations
issn 1417-3875
1417-3875
publishDate 2010-09-01
description This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for $t > 0$ and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.
url http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=518
work_keys_str_mv AT tokadiagana ontheexistenceofmildsolutionstosomesemilinearfractionalintegrodifferentialequations
AT gmmophou ontheexistenceofmildsolutionstosomesemilinearfractionalintegrodifferentialequations
AT gastonnguerekata ontheexistenceofmildsolutionstosomesemilinearfractionalintegrodifferentialequations
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