Optimal Control of Riemann–Liouville Fractional Stochastic Systems with Three-Parameter Damping

This paper studies mild solutions and Bolza optimal control for Riemann–Liouville fractional stochastic integro-differential systems incorporating fourth-order diffusion, time-varying control, non-instantaneous impulses, and infinite delay. Based on our self-developed (μ,ν,ξ,e,k)-resolvent family, we derive the mild solution formulation and prove its existence via the Krasnoselskii–Schaefer fixed-point theorem. Using the Arzela´-Ascoli theorem, Mazur’s lemma, and Balder’s lower semicontinuity principle, we further establish the existence of optimal control pairs. A numerical example from Euler–Bernoulli beam dynamics illustrates the theoretical results.