, Volume 70, Issue 3, pp 333-361
Date: 01 Feb 2011

Fractional Abstract Cauchy Problems

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This paper is concerned with fractional abstract Cauchy problems with order \({\alpha\in(1,2)}\) . The notion of fractional solution operator is introduced, its some properties are obtained. A generation theorem for exponentially bounded fractional solution operators is given. It is proved that the homogeneous fractional Cauchy problem (FACP 0) is well-posed if and only if its coefficient operator A generates an α-order fractional solution operator. Sufficient conditions are given to guarantee the existence and uniqueness of mild solutions and strong solutions of the inhomogeneous fractional Cauchy problem (FACP f ).

This work was supported by the Natural Science Foundation of China under the contact No. 60970149.