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On the local fractional derivative. (English) Zbl 1196.26011

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.

MSC:

26A33 Fractional derivatives and integrals
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