Geodesic
The global existence of mild solutions for semilinear fractional Cauchy problems in the $\alpha $-norm
Rong-Nian Wang1 ; De-Han Chen1 ; Yan Wang1
1Department of Mathematics NanChang University NanChang, JiangXi 330031, P.R. China
Annales Polonici Mathematici, Tome 103 (2012) no. 2, pp. 161-173
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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.
DOI : 10.4064/ap103-2-4
Keywords: study local global existence mild solutions class semilinear fractional cauchy problems alpha norm assuming operator linear part generator compact analytic semigroup suitable notion mild solution class problems introduced results obtained generalization continuation recent results issue

Rong-Nian Wang  1   ; De-Han Chen  1   ; Yan Wang  1

1 Department of Mathematics NanChang University NanChang, JiangXi 330031, P.R. China 
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     title = {The global existence of mild solutions for
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Rong-Nian Wang; De-Han Chen; Yan Wang. The global existence of mild solutions for
 semilinear fractional Cauchy problems in the $\alpha $-norm. Annales Polonici Mathematici, Tome 103 (2012) no. 2, pp. 161-173. doi: 10.4064/ap103-2-4

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