Since the nth order integral finds the volume enclosed by an n dimensional function, does that imply that fractional order integrals can be used to find the volume enclosed by rational (or irrational) dimensional functions, such as fractals?
I suppose that a problem with this definition is that fractals are not characterised by continuous functions and are usually just defined by recurrence relations. So are there any special cases where the fractional order integrals can be used to find the area of certain fractals?