Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces
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- 作者：Pengyu Chen (1)
Yongxiang Li (1)
1. Department of Mathematics ; Northwest Normal University ; Lanzhou聽 ; 730070 ; People鈥檚 Republic of China - 关键词：Fractional stochastic evolution equations ; Nonlocal condition ; Compact analytic semigroup ; Fractional power space ; Wiener process ; 35R11 ; 47J35 ; 60H15
- 刊名：Collectanea Mathematica
- 出版年：2015
- 出版时间：January 2015
- 年：2015
- 卷：66
- 期：1
- 页码：63-76
- 全文大小：200 KB
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- 刊物主题：Mathematics
Algebra
Analysis
Applications of Mathematics
Geometry - 出版者：Springer Milan
- ISSN：2038-4815
文摘
This paper is concerned with the existence of \(\alpha \) -mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space. We assume that the linear part generates a compact, analytic and uniformly bounded semigroup, the nonlinear part satisfies some local growth conditions in Hilbert space \(\mathbb {H}\) and the nonlocal term satisfies some local growth conditions in fractional power space \(\mathbb {H}_\alpha \) . The result obtained in this paper improves and extends some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract result.