Your formatting isn't completely clear to me, but this may help.
julia> my_date_strs=["20130628,2","20130701,3","19970224,4","19990230,5"]
4-element Array{ASCIIString,1}:
"20130628,2"
"20130701,3"
"19970224,4"
"19990230,5"
julia> my_dates=[date(my_d[1:4]*"-"*my_d[5:6]*"-"*my_d[7:8]) for my_d
inmy_date_strs
]
4-element Array{Date{C<:Calendar},1}:
2013-06-28
2013-07-01
1997-02-24
1999-03-02
julia> diff(my_dates)
3-element Array{Any,1}:
3 days
-5971 days
736 days
julia> my_dates[2]-my_dates[1]
3
julia> my_dates[2]-my_dates[1] |> typeof
Day{ISOCalendar}