Geodesic
Mild solutions for semilinear fractional differential equations
Electronic journal of differential equations, Tome 2009 (2009)
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.
Classification : 34K05, 34A12, 34A40
Keywords: fractional differential equation 
@article{EJDE_2009__2009__a82,
     author = {Mophou,  Gisele M. and N'Guerekata,  Gaston M.},
     title = {Mild solutions for semilinear fractional differential equations},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1179.34002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a82/}
}
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Mophou,  Gisele M.; N'Guerekata,  Gaston M. Mild solutions for semilinear fractional differential equations. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a82/