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The existence and uniqueness of mild solutions for a fractional stochastic differential system derived by Atangana–Baleanu fractional derivative have been discussed in a Hilbert space. A new set of results is obtained with non-Lipschitz conditions of nonlinear functions using the well-known Picard-type iterations, basic concepts of fractional calculus, sectorial operator, and stochastic analysis techniques. At last, an application is discussed to show the applicability of the developed theory.

Some existence results for a stochastic differential system with non-Lipschitz conditions