A remark on local fractional calculus and ordinary derivatives
  In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly. 
Ricardo Almeida, Malgorzata Guzowska, Tatiana Odzijewicz
math.CA