Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses

The current study discusses the approximate solutions for a class of fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses (NIIs) defined on a separable Hilbert space. The approximation to the nonlinear functions is obtained using orthogonal projection operator. The existence and convergence of the sequence of approximate solutions is proved using a fixed point theorem and analytic semigroup theory. Moreover, we show that finite-dimensional approximations converge, guaranteeing both computational feasibility and theoretical soundness. This study emphasises on short-memory systems, which are very significant for modelling fading memory effects. We demonstrate the practical importance and versatility of our method by applying it on fractional stochastic Burgers' and subdiffusion equations.