Article ID Journal Published Year Pages File Type
4617939 Journal of Mathematical Analysis and Applications 2012 11 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis