Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces

• Autores: Pengyu Chen, Yongxiang Li
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 1, 2015, págs. 63-76
• Idioma: inglés
• DOI: 10.1007/s13348-014-0106-y
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• Resumen

  • 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.