Theoretical Study of Applications of Fractional Calculus in Electromagnetism

建议编号：ECS-9612634首席研究员：Nader Engheta标题：分数阶微积分在电磁学中应用的理论研究在这项研究中，将开展一项使用分数阶微积分方法研究感兴趣的波和几何的理论研究。分数阶微积分方法使研究具有中间性质的波和结构成为可能。这是一个在国际和平倡议的重大贡献下发展起来的领域。在本研究中，将研究以下主题：(1)“分数”中间源；(2)分数阶微积分在电磁散射中的应用。将对入射平面波产生分数特征散射波的几何和边界进行双重研究，反之，从各种几何形状对具有分数特征的入射波进行散射。在这些领域中的每一个领域，理论本身的新的相应发展将被研究：(1‘)涉及电和磁分数阶多极和/或口径场的复源的分数阶多极子概念的推广和(2’)“分数”旋度算符的发展，如(2)所述，用于分析电磁散射相互作用，并用于研究波的分数特征和几何的对偶性所涉及的基本概念。

Proposal Number: ECS-9612634 Principal Investigator: Nader Engheta Title: Theoretical study of applications of fractional calculus in electromagnetism In this research, a theoretical investigation using the fractional calculus approach to waves and geometries of interest will be developed. The fractional calculus approach enables the study of waves and structures with an intermediate character. It is an area which has been developed with major contributions from the PI. Under the present study, the following topics will be investigated: (1) "fractional" intermediate sources and (2) applications of fractional calculus in electromagnetic scattering. Dual investigations of geometries and boundaries for which an incident plane waves generates scattered waves with fractional characteristics, and, conversely the scattering of incident waves with fractional characteristics from various geometries will be carried out. In each of these areas, a new corresponding development of the theory itself will be investigated (1') extension of the concept of fractional order multipoles for complex sources involving electric and magnetic fractional-order multipoles and/or aperture fields and (2') the development of a "fractional" curl operator, both for analysis of the electromagnetic scattering interactions as stated in (2) and for investigation the basic concepts involved in the duality of the fractional character of the waves and the geometries.