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On the existence of mild solutions to some semilinear fractional integro-differential equations. (English) Zbl 1211.34094
Summary: 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, 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.
MSC:
34K30Functional-differential equations in abstract spaces
34A08Fractional differential equations
34K10Boundary value problems for functional-differential equations