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Methods in Electromagnetics

Fractional Dual Solutions Using Calculus of Differential Forms

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Pages 399-410 | Published online: 03 Apr 2012

References

  • Gibbs , J. W. and Wilson , E. B. 1960 . Vector Analysis , New York : Dover . Reprint of the 1909 edition
  • Lindell , I. V. 1995 . Methods for Electromagnetic Field Analysis , 2nd edition , New York : IEEE Press .
  • Flanders , H. 1963 . Differential Forms , New York : Academic Press .
  • Thirring , W. 1979 . Classical Field Theory , New York : Springer .
  • Schutz , B. 1980 . Geometrical Methods of Mathematical Physics , Cambridge : University Press .
  • Warnick , K. F. , Selfridge , R. H. and Arnold , D. V. 1997 . Teaching electromagnetic field theory using differential forms . IEEE Transactions on Education , Vol. 40 ( No. 1 ) Feb : 63 – 68 .
  • Deschamps , J. A. 1981 . Electromagnetics and differential forms . Proc. of IEEE , Vol. 69 ( 6 ) June
  • Lindell , I. V. 2004 . Differential Forms in Electromagnetics , New York : IEEE Press .
  • Lindell , I. V. 2005 . Electromagnetic wave equation in differential-form representation . Progress In Electromagnetics Research , PIER 54 : 321 – 333 .
  • Lindell , I. V. 2006 . Electromagnetic fields in self-dual media in differential-form representation . Progress In Electromagnetics Research , PIER 58 : 319 – 333 .
  • Lindell , I. V. 2006 . The class of bi-anisotropic IB-media . Progress In Electromagnetics Research , PIER 57 : 1 – 18 .
  • Lindell , I. V. 2006 . Inverse for the skewon medium dyadic . Progress In Electromagnetics Research , PIER 63 : 21 – 32 .
  • Oldham , K. B. and Spanier , J. 1974 . The Fractional Calculus , New York : Academic Press .
  • Engheta , N. 1996 . On fractional calculus and fractional multipoles in electromagnetism . IEEE Trans. Antennas Propagation , 44 ( 4 ) : 554 – 566 .
  • Engheta , N. 1997 . On the role of fractional calculus in electromagnetic theory . IEEE Antennas and Propagation Magazine , Vol. 39 ( 4 ) August : 35 – 46 .
  • Engheta , N. 1998 . Fractional curl operator in electromagnetics . Microwave and Optical Technology Letters , Vol. 17 ( No. 2 ) February 5 : 86 – 91 .
  • Engheta , N. 1999 . On fractional paradigm and intermediate zones in electromagnetism: I. Planar observation . Microwave and Optical Technology Letters , Vol. 22 ( No. 4 ) August 20 : 236 – 241 .
  • Engheta , N. 1999 . On fractional paradigm and intermediate zones in electromagnetism: II. Cylindrical and spherical observations . Microwave and Optical Technology Letters , Vol. 23 ( No. 2 ) Oct 20 : 100 – 103 .
  • Engheta , N. 1999 . “ Fractional paradigm in electromagnetic theory ” . In Frontiers in Electromagnetics , Edited by: Werner , D. H. and Mittra , R. 523 – 552 . IEEE Press . Chapter 12
  • Ozaktas , H. M. , Zalevsky , Z. and Kutay , M. A. 2001 . The Fractional Fourier Transform with Applications in Optics and Signal Processing , New York : Wiley .
  • Naqvi , Q. A. , Murtaza , G. and Rizvi , A. A. 2000 . Fractional dual solutions to Maxwell equations in homogeneous chiral medium . Optics Communications , 178 : 27 – 30 .
  • Naqvi , Q. A. and Abbas , M. 2004 . Complex and higher order fractional curl operator in electromagnetics . Optics Communications , 241 : 349 – 355 .
  • Hussain , A. and Naqvi , Q. A. 2006 . Fractional curl operator in chiral medium and fractional nonsymmetric transmission line . Progress In Electromagnetics Research , PIER 59 : 199 – 213 .
  • Hussain , A. , Ishfaq , S. and Naqvi , Q. A. 2006 . Fractional curl operator and fractional waveguides . Progress In Electromagnetic Research , PIER 63 : 319 – 335 .
  • Hussain , A. , Faryad , M. and Naqvi , Q. A. 2007 . Fractional curl operator and fractional chiro-waveguide . Journal of Electromagnetic Waves and Applications , Vol. 21 ( 8 ) : 1119 – 1129 .
  • Naqvi , Q. A. and Abbas , M. 2003 . Fractional duality and metamaterials with negative permittivity and permeability . Optics Communications , 227 : 143 – 146 .
  • Naqvi , Q. A. and Rizvi , A. A. 2000 . Fractional dual solutions and corresponding sources . Progress In Electromagnetic Research , PIER 25 : 223 – 238 .
  • Naqvi , S. A. , Naqvi , Q. A. and Hussain , A. 2006 . Modelling of transmission through a chiral slab using fractional curl operator . Optics Communications , 226/2 : 404 – 406 .
  • Hussain , A. , Naqvi , Q. A. and Abbas , M. 2007 . Fractional duality and perfect electromagnetic conductor (PEMC) . Progress In Electromagnetics Research , PIER 71 : 85 – 94 .
  • Hussain , A. and Naqvi , Q. A. 2007 . Perfect electromagnetic conductor (PEMC) and fractional waveguide . Progress In Electromagnetics Research , PIER 73 : 61 – 69 .
  • Naqvi , S. A. , Faryad , M. , Naqvi , Q. A. and Abbas , M. 2008 . Fractional duality in homogeneous bi-isotropic medium . Progress In Electromagnetics Research , PIER 78 : 159 – 172 .
  • Ivakhnychenko , M. V. , Veliev , I. V. and Ahmedov , T. M. 2007 . Fractional operators approach in electromagnetic wave reflection approach . Journal of Electromagnetic Waves and Applications , Vol. 21 ( 13 ) : 1787 – 1802 .

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