Atangana-Baleanu fractional derivative applied to electromagnetic waves in dielectric media

Abstract

This work presents alternative solutions of the fractional waves in dielectric media using the Atangana–Baleanu fractional operator in Liouville-Caputo and Riemann–Liouville sense, the order considered is for the space-time domain. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. New results are presented and the analytical solutions are given in terms of the multivariate Mittag-Leffler functions preserving the physical units of the system studied. Numerical simulations were performed for different values of fractional order.

Keywords:

• Atangana-Baleanu fractional operators
• dielectric media
• Laplace transform
• Mittag-Leffler Function
• wave propagation

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

We would like to thank to Mayra Martínez for the interesting discussions. This work was supported by CONACYT. José Francisco Gómez Aguilar acknowledges the support provided by CONACYT: catedras CONACYT para jovenes investigadores 2014.