Generalized Riccati Wick differential equation and applications

Using the Wick derivation operator and the Wick product of elements in a distribution space $${\mathcal {F}}_\theta ^*({\mathcal {S}}'_{{\mathbb {C}}})$$ , we introduce the generalized Riccati Wick differential equation as a distribution analogue of the classical Riccati differential equation. The solution of this new equation is given. Finally, we finish this paper by building some applications.