J. Nonl. Evol. Equ. Appl. 2016 (4), pp. 55-69, published on November 29, 2016:

Quadratic Mean Almost Periodic Mild solutions to Fractional Stochastic Differential Equations in Hilbert Spaces

M. Kerboua

Guelma University, Department of Mathematics, Algeria

Received on December 1, 2015
Accepted on May 29, 2016

Communicated by Gisèle M. Mophou

Abstract.  In this paper, we prove the existence and uniqueness of quadratic mean almostperiodic mild solutions for a class of fractional stochastic differential equations of Sobolev type in a real separable Hilbert space. To establish our main results, we use the Banach contraction mapping principle, fractional calculus, stochastic analysis and an analytic semigroup of linear operators. An example is given to illustrate the theory.
Keywords:Stochastic fractional differential equations, quadratic mean almost periodic, analytic semigroups of linear operators.
2010 Mathematics Subject Classification:   34K14, 60H10, 35B15, 34F05, 34K50, 93B05.

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