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Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces

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Abstract

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.

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Acknowledgments

The authors would like to express his warmest thanks to the anonymous referees for carefully reading the manuscript and giving valuable comments and suggestions to improve the results of the paper. This work is supported by NNSF of China (11261053) and NSF of Gansu Province (1208RJZA129).

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou , 730070, People’s Republic of China

    Pengyu Chen & Yongxiang Li

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  1. Pengyu Chen
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  2. Yongxiang Li
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Correspondence to Pengyu Chen.

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Chen, P., Li, Y. Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces. Collect. Math. 66, 63–76 (2015). https://doi.org/10.1007/s13348-014-0106-y

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  • DOI: https://doi.org/10.1007/s13348-014-0106-y

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