Answer
Glucose oxidase acts only on $\beta$-D Glucose, but as the reaction proceeds and $\beta$-D Glucose decrease in concentration, $\alpha$-D Glucose will be converted into $\beta$-D Glucose by the process of mutarotation, and thus all glucose molecules will eventually be acted upon by Glucose oxidase.
Fehling's reaction is non-specific as it answers positive to other reducing sugars, but glucose oxidase reacts only with glucose.
Work Step by Step
Mutarotation is the process of conversion between $\beta$-D Glucose and $\alpha$-D Glucose