Regularity theory for a new class of fractional parabolic stochastic evolution equations

A new class of fractional-order parabolic stochastic evolution equations of the form (∂t+A)γX(t)=W˙Q(t) , t∈ [0 , T] , γ∈ (0 , ∞) , is introduced, where - A generates a C -semigroup on a separable Hilbert space H and the spatiotemporal driving noise W˙ ^Q is the formal time derivative of an H-valued cylindrical Q-Wiener process....