Local fractional Moisil-Teodorescu operator in quaternionic setting involving Cantor-type coordinate systems

Abstract

In this paper, general quaternionic structure are developed for the local fractional Moisil-Teodorescu operator in Cantor-type cylindrical and spherical coordinate systems. Two examples for the Helmholtz equation with local fractional derivatives on the Cantor sets are shown by making use of this local fractional Moisil-Teodorescu operator.