Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617939 | Journal of Mathematical Analysis and Applications | 2012 | 11 Pages |
Abstract
Motivated by an equality of the Mittag–Leffler function proved recently by the authors, this paper develops an operator theory for the fractional abstract Cauchy problem (FACP) with order α∈(0,1). The notion of fractional semigroup is introduced. It is proved that a family of bounded linear operator is a solution operator for (FACP) if and only if it is a fractional semigroup. Moreover, the well-posedness of the problem (FACP) is also discussed. It is shown that the problem (FACP) is well-posed if and only if its coefficient operator generates a fractional semigroup.
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