Journal
JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS
Volume 29, Issue 6, Pages 727-740Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/09205071.2015.1016189
Keywords
anomalous behavior; caputo derivative; fractional differential equations; dielectric media; dynamical system modeling; wave propagation; Mittag-Leffler function
Funding
- CONACYT
- CONACYT: catedras CONACYT para jovenes investigadores
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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 [GRAPHICS] , 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 [GRAPHICS] and [GRAPHICS] preserving the appropriated physical units according to the system studied.
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