Universal character of the fractional space-time electromagnetic waves in dielectric media

Abstract

This work presents an alternative solution for the mathematical analysis of the fractional waves in dielectric media. For the fractional wave equation, the Caputo fractional derivative was considered, the order of the spatial and temporal fractional derivatives are , respectively. In this analysis, we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space and time derivatives into the fractional wave equation. We will consider source free Maxwell equations in isotropic and homogeneous dielectric medium. The general solutions obtained in our research have been expressed in terms of the multivariate Mittag–Leffler functions, these functions depend only on the parameters and preserving the appropriated physical units according to the system studied.

Keywords:

• dynamical system modeling
• dielectric media
• caputo derivative
• Mittag–Leffler function
• anomalous behavior
• wave propagation
• fractional differential equations

Acknowledgements

We would like to thank Mayra Martínez and Prof. Dumitru Baleanu for the interesting discussions.

Additional information

Funding

This work was supported by CONACYT. José Francisco Gómez Aguilar acknowledges the support provided by CONACYT: catedras CONACYT para jovenes investigadores 2014.