The global existence of mild solutions for semilinear fractional Cauchy problems in the $\alpha $-norm

Volume 103 / 2012

Rong-Nian Wang, De-Han Chen, Yan Wang 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.

Authors

  • Rong-Nian WangDepartment of Mathematics
    NanChang University
    NanChang, JiangXi 330031, P.R. China
    e-mail
  • De-Han ChenDepartment of Mathematics
    NanChang University
    NanChang, JiangXi 330031, P.R. China
    e-mail
  • Yan WangDepartment of Mathematics
    NanChang University
    NanChang, JiangXi 330031, P.R. China
    e-mail

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