Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 21, pp. 1-9.

Title: Mild solutions for semilinear fractional differential equations
   
Authors: Gisele  M. Mophou (Univ. des Antilles, Guadeloupe)
         Gaston M. N'Guerekata  (Morgan State Univ., Baltimore, MD, USA

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.