TY - JOUR
T1 - Fractional Abstract Cauchy Problems
AU - Kexue, Li
AU - Jigen, Peng
PY - 2011/7
Y1 - 2011/7
N2 - This paper is concerned with fractional abstract Cauchy problems with order α (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 (FACP0) 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 (FACPf).
AB - This paper is concerned with fractional abstract Cauchy problems with order α (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 (FACP0) 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 (FACPf).
KW - Caputo fractional derivative
KW - Riemann-Liouville fractional derivative
KW - Riemann-Liouville fractional integral
KW - fractional abstract Cauchy problem
KW - fractional solution operator
UR - https://www.scopus.com/pages/publications/79959193516
U2 - 10.1007/s00020-011-1864-5
DO - 10.1007/s00020-011-1864-5
M3 - 文章
AN - SCOPUS:79959193516
SN - 0378-620X
VL - 70
SP - 333
EP - 361
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 3
ER -