Abstract
In this paper, we study the existence and uniqueness of Hadamard Ito-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard it-eration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the conver-gence of the solution of the averaged HIDSFOS to that of the standard HIDS-FOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results.