This paper presents a Caputo fractional-order SEIR epidemic model of order in which the latent period enters as a discrete delay in the incidence, environmental variability acts as multiplicative white noise on the infectious class, and a time-dependent vaccination effort is applied to the susceptible class. The model is written in its stochastic Volterra form, and the restriction , under which the stochastic convolution against the singular kernel has finite variance, is shown to govern both the well-posedness of the model and the mean-square convergence of its discretisation. Local existence and uniqueness are obtained by a contraction argument; the solution is then continued globally by the method of steps, which exploits the fact that the delayed incidence is linear on each delay window, and the moments of the total population are controlled through a Mittag-Leffler resolvent representation, so that the demographic balance law holds in expectation. Positivity of the noisy compartment is proved for the deterministic model and for the classical order, and is adopted as an explicit hypothesis, supported by numerical evidence, for the fractional stochastic case. The basic reproduction number R₀ is derived from the next-generation matrix. When R₀ < 1, the disease-free equilibrium of the deterministic skeleton is globally asymptotically stable and the infected classes of the stochastic model vanish in the mean, for every delay and every noise intensity. When R₀ > 1, a unique endemic equilibrium exists, is globally asymptotically stable in the absence of delay and, by a modulus estimate on the characteristic quasi-polynomial, remains locally asymptotically stable for every delay, so that latency alone cannot destabilise the endemic state through a Hopf bifurcation. For the classical order, an explicit noise threshold depending on the delay is derived, beyond which the infection dies out almost surely at an exponential rate. An optimal vaccination problem is formulated, the existence of an optimal control is proved, and the optimal policy is characterised through a maximum principle whose adjoint system is a backward Volterra equation carrying a time-advanced term. A fractional predictor-corrector scheme with a fractional Euler-Maruyama step is described, its convergence orders are verified through error tables, and simulations quantify the influence of the fractional order, the delay, the noise intensity, the transmission rate and the vaccination policy on the course of the epidemic.