Existence results for a coupled system of fractional stochastic differential equations involving Hilfer derivative

In this paper, we consider a coupled system of fractional stochastic differential equations involving the Hilfer derivative of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo><</m:mo> <m:mi>α</m:mi> <m:mo><</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {1/2<α<1} . Under some assumptions, we prove the existence of mild solutions for our system based on Perov’s and Schaefer’s fixed point theorems. An example illustrating our result is provided.