Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays

This paper is concerned with stochastic differential equations of fractional-order q ∈(m-1, m) (where m ∈ Z and m ≥ 2 ) with finite delay at a space BC ( [ - τ, 0];Rᵈ ) . Some sufficient conditions are obtained for the existence and uniqueness of solutions for these stochastic fractional differential systems by applying the Picard iterations method and the generalized Gronwall inequality.