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

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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