Fractionalization methods and their applications to radiation and scattering problems

Abstract

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory. Fractional calculus is a branch of mathematics that addresses the mathematical properties of operation of fractional differentiation and fractional integration operators involving derivatives and integrals to arbitrary non-integer orders. We have applied the tools of fractional calculus in various problems in electromagnetic fields and waves, and have obtained interesting results that highlight certain notable features and promising potential applications of these operators in electromagnetic theory. Moreover, since fractional derivatives/integrals are effectively the result of fractionalization of differentiation and integration operators, we have investigated the notion of fractionalization of some other linear operators in electromagnetic theory. Searching for such operator fractionalization has led us to interesting solutions in radiation and scattering problems.