ELECTROSTATIC FRACTIONAL IMAGE METHODS FOR PERFECTLY CONDUCTING WEDGES AND CONES

In our earlier work, we introduced a definition for the electric charg e ''fractional-order'' multipoles using the concept of fractional deri vatives and integrals [1], Here, we utilize that definition to introdu ce a detailed image theory for the two-dimensional (2-D) electrostatic potential distributions in front of a perfectly conducting wedge with arbitrary wedge angles, and for the three-dimensional potential in fr ont of a perfectly conducting cane with arbitrary cone angles, We show that the potentials in the presence of these structures can be descri bed equivalently as the electrostatic potentials of sets of equivalent ''image'' charge distributions that effectively behave as ''fractiona l-order'' multipoles; hence, the name ''fractional'' image methods, Th e fractional orders of these so-called fractional images depend on the wedge angle (for the wedge problem) and on the cone angle (for the co ne problem), Special cases where these fractional images behave like t he discrete images are discussed, and physical justification and insig hts into these results are given.