Minkowski distance and pdist

Minkowski's distance equation can be found here.

If we want to calculate the Minkowski distance in MATLAB, I think we can do the following (correct me if I'm wrong):

dist=pdist([x(i);y(j)],'minkowski');

Up till here, the above command will do the equation shown in the link.

Now, to Minkowski's distance, I want to add this part -m(i)^m, where m(i) is some value.

I saw the pdist source code, but, want to ask, how can I modify Minkowski's distance by adding this simple part, either in the pdist code, or from the calling code (I think we may have to make some change in the parameters).

Thanks.