Electron. J. Diff. Eqns., Vol. 2009(2009), No. 21, pp. 1-9.

Mild solutions for semilinear fractional differential equations

Gisele M. Mophou, Gaston M. N'Guerekata

Abstract:
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.

Submitted October 28, 2008. Published January 23, 2009.
Math Subject Classifications: 34K05, 34A12, 34A40.
Key Words: Fractional differential equation.

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Gisèle M. Mophou
Université des Antilles et de la Guadeloupe
Département de Mathématiques et Informatique
Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI)
email: gmophou@univ-ag.fr
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu

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