A novel characteristic of solution operator for the fractional abstract Cauchy problem

作者：Peng Jigen^*; Li Kexue

来源：Journal of Mathematical Analysis and Applications, 2012, 385(2): 786-796.

DOI：10.1016/j.jmaa.2011.07.009

• Fractional abstract Cauchy problem
• Fractional derivative
• Fractional semigroup
• Solution operator

Motivated by an equality of the Mittag-Leffier function proved recently by the authors, this paper develops an operator theory for the fractional abstract Cauchy problem (FACP) with order alpha is an element of (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.

• 出版日期2012-1-15
• 单位西安交通大学