  This manuscript proposes a class of fractional stochastic
integro-differential equation (FSIDE) with non-instantaneous impulses in an
arbitrary separable Hilbert space. We use a projection scheme of increasing
sequence of finite dimensional subspaces and projection operators to define
approximations. In order to demonstrate the existence and convergence of an
approximate solution, we utilize stochastic analysis theory, fractional
calculus, theory of fractional cosine family of linear operators and fixed
point approach. Furthermore, we examine the convergence of Faedo-Galerkin(F-G)
approximate solution to the mild solution of our given problem. Finally, a
concrete example involving partial differential equation is provided to
validate the main abstract results.
