Ta'anis 26b - Nesias Kapayim by Mincha of a fast day

The gemara comments that we duchan by mincha on a fast since there is no concern of drunkenness, and since we daven close to sunset, mincha is associated with neila and there is no concern that it will lead to duchening by mincha the rest of the year. It would seem that if one davens mincha k'tana on a fast, they should certainly duchan (in e.y. of course). However, rashi seems to explain that this is only when one normally davens mincha g'dola and on the fast is davening mincha k'tana, but if one normally davens mincha k'tana then they should not duchen on a fast even if they daven mincha k'tana. Nevertheless, following the simple understanding of the gemara, it would seem that if one daven mincha k'tana on a ta'anis, there is duchaning.

But, if one davens mincha g'dola on a fast, one should not duchen (even if the rest of the year they normally daven mincha k'tana so there is a heker, it seems from the gemara that its not sufficient, bec. we also need the sevara of being similar or in the place of neila).

The Chazon Ish (O.C. 20) suggests that even if one davens mincha g'dola they should duchan bec. at the close of the talmud the decision was to duchan at mincha of a fast. (He raises that the Ritvah seems to imply otherwise, but then explains that the Ritvah is speaking in a time where neillah is said so if duchaning was done by mincha g'dola it would be clear that there should be duchaning by mincha and will lead to duchaning by mincha on other days. But if there is no neillah, like by our fast days, then one should duchan by mincha since it will be understood that it is to make up for not duchaning by neillah).

The Steipler testifies that the Chazon Ish did allow duchaning even my m.g. on a ta'anis.