Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

被引：0
作者：
Rong-Nian Wang
Jun Liu
De-Han Chen
机构：
[1] NanChang University,Department of Mathematics
来源：
Advances in Difference Equations | / 2011卷
关键词：
Cauchy problem of abstract fractional evolution equation; Nonlocal initial condition; Fixed point theorem; Mild solution; -norm;
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摘要：
In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered.
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