On the local fractional derivative
The authors focus on the right (left) local fractional derivatives defined by Kolwankar and Gangal (KG-LFD). They introduce more general but weaker notions of LFDs by using limits of certain integral averages of the difference-quotient. They establish a structural theorem which says that if both the right and left KG-LFDs exists a.e. in an interval, then they are both zero a.e. in this interval. They also make a partial extension of the one dimensional result to higher dimensional cases.
scientific article; zbMATH DE number 5640352