In this paper, we are concerned with a class of stochastic  differential equations with a discontinuous drift driven by fractional Brownian motion with Hurst parameter 1/2<H<1. By approximation arguments and a comparison theorem, we prove the existence  of solutions for this kind of equations under the linear growth condition. Subsequently, by defining a suitable stochastic tangent cone, we obtain a viability result for the considered stochastic systems with discontinuous shift coefficient. The sufficient and necessary condition is also an alternative global existence result for the fractional differential equations with restrictions on the state.

     Finally, by direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution for the coupled stochastic systems under investigation evolves in some particular sets.

 

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