Modify alpha opacity of LESS variable

For completeness

fade

Set the absolute transparency of a color. Can be applied to colors whether they already have an opacity value or not.

background: fade(@blue, 20%);

fadein

Decrease the transparency (or increase the opacity) of a color, making it more opaque.

background: fadein(@blue, 80%);

fadeout

Increase the transparency (or decrease the opacity) of a color, making it less opaque. To fade in the other direction use fadein.

background: fadeout(@blue, 20%);

View Complete Documentation

The site documentation gives the answer:

background: fade(@blue, 20%);

The function name is fade not alpha according to that document.