Can we oxidize aliphatic alkane to produce carboxylic acid?
It's tricky, because the bond enthalpies of sp3 C-H bonds are high (so they are hard to break) and because alkanes typically have a large number of CH bonds so selectively oxidizing any one of them can be challenging. Generally speaking the more electron-rich CH bonds (i.e. tertiary positions) are oxidized more easily that less-substituted, less electron rich ones.

TFDO will do it, see here: https://en.wikipedia.org/wiki/Oxidation_with_dioxiranes and there are a bunch of other methods (just try googling "aliphatic CH oxidation"). 

It's quite a hot area of research, since if you can control it then in theory you can turn feedstocks from crude oil into more useful functionalized molecules.