Approximation of solutions to fractional stochastic integro-differential equations of order α ∈ (1,2].

This paper is concerned with the approximation of the solutions to fractional stochastic integro-differential equations with finite delay in a separable Hilbert space. With the help of projection operator, we construct the finite dimensional approximate solutions of the given system. The theory of α-order cosine family of linear operators and stochastic version of the well-known Banach fixed point theorem are applied to show the existence and uniqueness of approximate solution. At last, we show that these approximate solutions form a Cauchy sequence with respect to an appropriate norm, and the limit of this sequence is a solution of the original problem. Moreover, we show the convergence of Faedo-Galerkin approximate solution. Finally, we demonstrate an example to show the applications of these abstract results. [ABSTRACT FROM AUTHOR]