Fractionalization methods and their applications to radiation and scattering problems

International Conference on Mathematical Methods in Electromagnetic Theory, MMET

Volumn 1, Issue , 2000, Pages 34-40

  Engheta, N ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Current density; Electromagnetic fields; Electromagnetic radiation; Electromagnetic scattering; Fractional calculus; Mathematics; Maxwell equations; Vectors

Indexed keywords

CALCULATIONS; CURRENT DENSITY; DIFFERENTIATION (CALCULUS); ELECTRIC FIELDS; ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC WAVES; MATHEMATICAL OPERATORS; MATHEMATICAL TECHNIQUES; MAXWELL EQUATIONS; VECTORS;

ELECTROMAGNETIC SCATTERING; ELECTROMAGNETIC THEORIES; FRACTIONAL CALCULUS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIATION; FRACTIONAL INTEGRATION; INTEGRATION OPERATORS; MATHEMATICAL PROPERTIES;

ELECTROMAGNETIC FIELD THEORY;

EID: 14544305165     PISSN: 21611734     EISSN: 21611750     Source Type: Conference Proceeding    
DOI: 10.1109/MMET.2000.888504     Document Type: Conference Paper

References (13)

1. N. Engheta, "Fractional Paradigm in Electromagnetic Theory" a chapter in Frontiers in Electromagnetics, D. H. Werner and R. Mittra (eds.), IEEE Press, New York, chapter 12, pp. 523-552, (2000).
2. N. Engheta, "On Fractional Paradigm and Intermediate Zones in Electromagnetism: I. Planar Observation," in Microwave and Optical Technology Letters, Vol. 22, No. 4, pp. 236-241 (August 20, 1999).
3. N. Engheta, "On Fractional Paradigm and Intermediate Zones in Electromagnetism: II. Cylindrical and Spherical Observations," in Microwave and Optical Technology Letters, Vol. 23, No. 2, pp. 100-103 (October 20, 1999).
4. N. Engheta, "Phase and Amplitude of the Fractional-Order Intermediate Wave" in Microwave and Optical Technology Letters, Vol. 21, No. 5, pp. 338-343 (June 5, 1999).
5. N. Engheta, "Fractional Curl Operator in Electromagnetics," in Microwave and Optical Technology Letters, Vol. 17, No. 2, pp. 86-91 (February 5, 1998).
6. N. Engheta, "On Fractional Calculus and Fractional Multipoles in Electromagnetism," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 4, pp. 554-566 (April 1996).
7. N. Engheta, "Electrostatic "Fractional" Image Methods for Perfectly Conducting Wedges and Cones," in IEEE Transactions on Antennas and Propagation., Vol. 44, No. 12, pp. 1565-1574 (December 1996).
8. N. Engheta, "On the Role of Fractional Calculus in Electromagnetic Theory" a feature article in IEEE Antennas and Propagation Magazine, Vol. 39, No. 4, pp. 35-46 (August 1997).
9. N. Engheta, "Use of Fractional Integration to Propose Some "Fractional" Solutions for the Scalar Helmholtz Equation," a chapter in Progress in Electromagnetics Research (PIER) Monograph Series Vol. 12, Jin A. Kong (ed.), pp. 107-132 (1996).
10. N. Engheta, "A Note on Fractional Calculus and the Image Method for Dielectric Spheres," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 9, pp. 1179-1188 (September 1995).
11. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, (1974).
12. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, Langhorne, Pennsylvania, 1993. (Originally published in Russian by Nauka i Tekhnika, Minsk, 1987).
13. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.