TY - JOUR
T1 - A novel characteristic of solution operator for the fractional abstract Cauchy problem
AU - Peng, Jigen
AU - Li, Kexue
PY - 2012/1/15
Y1 - 2012/1/15
N2 - 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 ∈(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.
AB - 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 ∈(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.
KW - Fractional abstract Cauchy problem
KW - Fractional derivative
KW - Fractional semigroup
KW - Solution operator
UR - https://www.scopus.com/pages/publications/80052182566
U2 - 10.1016/j.jmaa.2011.07.009
DO - 10.1016/j.jmaa.2011.07.009
M3 - 文章
AN - SCOPUS:80052182566
SN - 0022-247X
VL - 385
SP - 786
EP - 796
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -