Theoretical Study of Applications of Fractional Calculus in Electromagnetism

项目编号：ECS-9612634首席研究员：Nader Engheta题目：分数阶微积分在电磁学中的应用理论研究在本研究中，将对分数阶微积分方法在波和感兴趣的几何中的应用进行理论研究。分数阶微积分方法使波浪和结构的研究具有中间性质。这是一个在PI的主要贡献下发展起来的领域。在本研究中，将研究以下主题：(1)分数阶中间源和(2)分数阶微积分在电磁散射中的应用。对入射平面波产生具有分数特征的散射波的几何形状和边界的双重研究，以及相反地，对来自各种几何形状的具有分数特征的入射波的散射将进行研究。在这些领域中，将研究理论本身的一个新的相应发展(1)涉及电和磁分数阶多极和/或孔径场的复杂源的分数阶多极概念的扩展和(2)“分数”旋度算子的发展；为了分析(2)中所述的电磁散射相互作用，以及为了研究波和几何形状的分数特征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.