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In this paper we study the properties of the solution of a stochastic nonlinear equation of Schrödinger type, which is perturbed by a cylindrical Wiener process and an additive cylindrical fractional Brownian motion with Hurst parameter in the interval (½, 1). The existence of the solution and the existence of the Malliavin derivative are proved.

Mathematics Subject Classification (2010): 60H15, 60H07, 35Q41.

Keywords: Nonlinear stochastic Schrödinger equations, cylindrical Wiener process, cylindrical fractional Brownian motion, Malliavin derivative.