Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 136, pp. 1-9.
Title: Existence of local and global solutions to some impulsive
fractional differential equations
Authors: Rahima Atmania (Univ. of Badji Mokhtar Annaba, Algeria)
Said Mazouzi (Univ. of Badji Mokhtar Annaba, Algeria)
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.
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.
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.