Existence results for mean-field stochastic integrodifferential equations driven by fractional Brownian motion

Abstract In this work, we study the existence and uniqueness of mild solution for a mean-field stochastic integrodifferential equation (SIDEs) with finite delay, driven by a fractional Brownian motion in a Hilbert space with Hurst parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="normal">H</m:mi> <m:mo>&gt;</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> </m:mrow> </m:math> {\mathrm{H}&gt;\frac{1}{2}} . We suppose that the linear part has a resolvent operator in the sense given in [R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 1982, 1, 333–349]. An example is provided to show the applicability of our results.