Rahima Atmania, Said Mazouzi
Abstract:
First, by using Schauder's fixed-point theorem we establish the
existence uniqueness of locals for some fractional differential
equation with a finite number of impulses. On the other hand,
by using Brouwer's fixed-point theorem, we establish existence of
the global solutions under suitable assumptions.
Submitted July 3, 2009. Published October 21, 2009.
Math Subject Classifications: 26A33, 34A12, 34A37.
Key Words: Fractional derivative; impulsive conditions; fixed point;
local solution; global solution.
An addendum was attached on August 31, 2010. It corrects some misprints and presents a new proof of Theorem 4.2. See the last page of this article.
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Rahima Atmania Laboratory of Applied Mathematics (LMA) Department of Mathematics, University of Badji Mokhtar Annaba P.O. Box 12, Annaba 23000, Algeria email: atmanira@yahoo.fr |
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Said Mazouzi Laboratory of Applied Mathematics (LMA) Department of Mathematics, University of Badji Mokhtar Annaba P.O. Box 12, Annaba 23000, Algeria email: mazouzi_sa@yahoo.fr |
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