Global attracting set of stochastic differential equations with unbounded delay driven by fractional Ornstein–Uhlenbeck process

In this paper, we have studied stochastic differential equations with unbounded delay in fractional power spaces perturbed by fractional Ornstein–Uhlenbeck process <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>Y</m:mi> <m:mrow> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:mi>ξ</m:mi> </m:mrow> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {{YH,ξ}(t)} with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>H</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {H∈(1/2,1)} . Subsequently, the existence and uniqueness of mild solution of the considered equation have been proved with fixed-point theorem. Finally, we obtain the global attracting set of the considered equations by some stochastic analysis and inequality technique.