Fractionalization Methods and their Applications to Radiation and Scattering Problems

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 in recent years. 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 (see e.g., [1-10]). 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 (see e.g., [11-13]). In our study in recent years, 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 [1-10]. 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. Comments Copyright 2000 IEEE. Reprinted from International Conference on Mathematical Methods in Electromagnetic Theory 2000 (MMET 2000) Volume 1, pages 34-40. Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=19211 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/15 34 M M E T * 2 0 0 0 P r o c e e d i n g s FRACTIONALIZATION METHODS AND THEIR APPLICATIONS TO RADIATION AND SCATTERING PROBLEMS Nader Engheta University of Pennsylvania Moore School of Electrical Engineering Philadelphia, Pennsylvania 191 04, U.S.A. Tel: + I (215) 898-9777, Fax: +1 (215) 573-2068 E-mail: engheta 0 ee.upenn.edu Web: http://www.ee.upenn.edu/-enghetaf