On the role of fractional calculus in electromagnetic theory

In this feature article, we have briefly reviewed some of the roles and applications of fractional calculus in electromagnetics that we have recently introduced and explored. These cases, although limited and specific in nature, might reveal interesting features of fractional derivatives and integrals and their possible utilities in electromagnetic theory. Since fractional derivatives/ integrals are effectively the intermediate case between the conventional integer-order differentiation/integration, one may speculate that use of these fractional operators in electromagnetics may provide interesting, novel, "intermediate" cases in electromagnetics. Cases such as fractional multipoles, fractional solutions for Helmholtz equations, and fractional-image methods are the ones that we have studied and briefly reviewed here. Some other cases, such as the fractionalization of the curl operator and its electromagnetic applications, are currently under study by the author. Preliminary results of this study will be presented in the upcoming IEEE AP-S International Symposium/URSI North American Radio Science Meeting in Montreal, Canada, in July, 1997.