The global existence of mild solutions for semilinear fractional Cauchy problems in the $\alpha $-norm
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 161-173
MSC: Primary 34K37; Secondary 26A33, 34A08.
DOI: 10.4064/ap103-2-4
Abstract
We study the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the $\alpha $-norm assuming that the operator in the linear part is the generator of a compact analytic $C_0$-semigroup. A suitable notion of mild solution for this class of problems is also introduced. The results obtained are a generalization and continuation of some recent results on this issue.
