Fractional Electromagnetic Fields in DPS and DNG Regions With Standard Fractional Vector Cross product: Fractional Electromagnetic Fields in DPS and DNG Regions With Standard Fractional Vector Cross product

Manisha Kankarej; Shashikant Pandey; Jai Pratap Singh

Authors

Dr. Kankarej Rochester Institute of Technology, Dubai
Dr. Pandey University of Lucknow
Professor Singh B. S. N. V. P. G. College, University of Lucknow https://orcid.org/0000-0002-0008-2339

Keywords:

Standard fractional vector cross product, DPS region, DNG region

Abstract

In this research we have obtained fractional electromagnetic fields in DPS and DNG regions using standard fractional vector cross product(SFVCP). We have also calculated fractional electromagnetic fields of a travelling electromagnetic wave in DPS and DNG region with oblique incidence using SFVCP. This approach is new as the definition of SFVCP is not yet explored for calculating fractional electromagnetic fields in DPS and DNG regions. This study will add a new dimension to the study of electromagnetic fields that have application in mobile communication, transmission from antenna, in lens design etc.

References

M. J. Crowe, A history of vector analysis, The evolution of the idea of a vectorial system, University of Notre Dame Press, Notre Dame, Ind.-London, 1967.

S. Das, Geometrically deriving fractional cross product and fractional curl, Int. J. Math. Comput. 20, no. 3, (2013), 1-29.

S. Das, Functional Fractional calculus, 2nd edition, Springer-Verlag, 2011.

R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge Univ. Press UK 1985.

M. Kankarej, J. P. Singh, Standard Fractional Vector Cross Product in Euclidean 3 - Space, communicated for consideration.

M. Kankarej, J. P. Singh, Fractional Curl With Standard Fractional Vector Cross Product for a Vector Pair, accepted for publication, Results in Non Linear Analysis, (2023).

M. Kankarej, J. P. Singh, Standard Fields With Standard Fractional Vector Cross Product, accepted for publication, Journal of Applied Mathematics and Informatics, (July 2023).

D. R. Smith, W. J. Padilla, D. C. Vier, Nemat-Nasser S. C.,Schultz S., Composite Medium with Simultaneously Negative Permeability and Permittivity, Physical Review Letters, vol. 84, 2000.

V. G. Veselago, The electrodynamics of substances with simultaneously negative values of $epsilon$ and $mu$, Soviet Physics Uspekhi, vol. 10, pp. 509-514, Jan.–Feb., 1968.

Fractional Electromagnetic Fields in DPS and DNG Regions With Standard Fractional Vector Cross product