Abstract
This manuscript proposes a class of fractional stochastic integro-differential equations (FSIDEs) 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 approximate solutions, 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 the Faedo–Galerkin (F–G) approximate solutions to the mild solution of our given problem. Finally, a concrete example involving a partial differential equation is provided to validate the main abstract results.
Acknowledgments
We are very thankful to the anonymous reviewers and associate editor for providing constructive comments and valuable suggestions to enhance the quality of this manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).