Asymptotic behavior of linear fractional stochastic differential equations with time-varying delays

• A general class of linear fractional stochastic differential equations with time-varying delays is considered.
• Using the method of semimartingale approximation, we prove a representation formula for the solution.
• A sufficient condition for the exponential asymptotic behavior of solutions is provided.

In this paper we give a sufficient condition for the exponential asymptotic behavior of solutions of a general class of linear fractional stochastic differential equations with time-varying delays. Our obtained results allow us to employ the theories developed for the deterministic systems and to illustrate this, some examples are provided.