`::If I still haven't answered your question: ``At what fractional does the fractional derivative does the non-smoothness make the fractional derivative locally undefined?`` - then let me just say that it's the same as non-fractional integration.  You're really not doing anything different, spatially speaking.  And the formalism only describes what's going on spatially, so if you try to measure the volume of a surface or something like that, you'll have problems.  Just so long as you realize what you're actually doing, there should be no surprises.  And one more thing: notice that integration has a region of integration, but differentiation doesn't.  That's why you have to add that ``C`` back in when you reverse it.  Same holds true for fractional integration, only the ``C`` might be a function of fractional dimension.  NASA invented an ``initialized fractional calculus`` to deal with this.  You might find it interesting.    `