Electron. J. Diff. Equ., Vol. 2009(2009), No. 136, pp. 1-9.

Existence of local and global solutions to some impulsive fractional differential equations

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
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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