On the existence of mild solutions to some semilinear fractional integro-differential equations

By Toka Diagana, Gisèle M. Mophou, Gaston M. N'Guérékata. 2010

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Abstract. This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for t > 0 and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.

Subfields: Applied Mathematics, Numerical Analysis

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