Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative

Abstract

In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.

Keywords

• brownian motion
• Caputo-Itô derivative
• Itô process
• existence
• uniqueness