222
Views
22
CrossRef citations to date
0
Altmetric
Articles

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

, , , , &
Pages 727-740 | Received 19 Nov 2014, Accepted 30 Jan 2015, Published online: 18 Mar 2015

References

  • Oldham KB, Spanier J. The fractional calculus. New York (NY): Academic Press; 1974.
  • Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. New York (NY): John Wiley; 1993.
  • Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
  • Baleanu D, Diethelm K, Scalas E, Trujillo JJ. Fractional calculus models and numerical methods. Series on complexity, nonlinearity and chaos. Singapore: World Scientific; 2012.
  • Aguilar JG, Hernández MM. Space-time fractional diffusion-advection equation with caputo derivative. Abstr. Appl. Anal. 2014;1:8 pages. Article ID 283019.
  • Tohidi E, Bhrawy AH, Erfani K. A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation. Appl. Math. Model. 2013;37:4283–4294.
  • Gómez F, Bernal J, Rosales J, Córdova T. Modeling and simulation of equivalent circuits in description of biological systems – a fractional calculus approach. J. Electr. Bioimpedance. 2012;3:2–11.
  • Baleanu D, Golmankhaneh AK, Golmankhaneh AK, Nigmatullin RR. Newtonian law with memory. Nonlinear Dyn. 2010;60:81–86. Springer.
  • Gómez-Aguilar JF, Razo Hernández JR. Ley de enfriamiento de Newton de orden fraccionario. Revista Investigación y Ciencia de la Universidad Autónoma de Aguascalientes. 2014;22:12–18.
  • Hilfer R, editor. Applications of fractional calculus in physics. Singapore: World Scientific; 2000.
  • Rosales J, Guía M, Gómez F, Aguilar F, Martínez J. Two dimensional fractional projectile motion in a resisting medium. Cent. Eur. J. Phys. 2014;12:517–520.
  • Yang Xiao-Jun. Advanced local fractional calculus and its applications. New York (NY): World Science; 2012.
  • Uchaikin V. Fractional derivatives for physicists and engineers. New York (NY): Springer; 2012.
  • Riewe F. Nonconservative lagrangian and hamiltonian mechanics. Phys. Rev. E. 1996;53:1890–1899.
  • Muslih Sami I, Saddallah M, Baleanu D, Rabei E. Lagrangian formulation of maxwell’s field in fractional D dimensional space-time. Romanian J. Phys. 2010;55:659–663.
  • Baleanu D, Muslih Sami I, Rabei Eqab M. On fractional euler-lagrange and hamilton equations and the fractional generalization of total time derivative. Nonlinear Dyn. 2008;53:67–74. Springer.
  • Engheta Nader. Fractional curl operator in electromagnetics. Microw. Opt. Tech. Lett. 1998;17:86–91.
  • Hussain A, Faryad M, Naqvi QA. Fractional curl operator and fractional chiro-waveguide. J Electromagn. Waves Appl. 2007;21:1119–1129.
  • Naqvi SA, Naqvi QA, Hussain A. Modelling of transmission through a chiral slab using fractional curl operator. Optics Commun. 2006;266:404–406.
  • Naqvi QA, Abbas M. Complex and higher order fractional curl operator in electromagnetics. Optics Commun. 2004;241:349–355.
  • Tarasov VE. Fractional equations of curie-von schweidler and gauss laws. J. Phys. Condens. Matter. 2008;20:145–212.
  • Tarasov VE. Universal electromagnetic vaves in dielectric. J. Phys. Condens. Matter. 2008;20:175–223.
  • Coffey WT, Kalmykov YuP, Titov SV. Anomalous dielectric relaxation in the context of the debye model of noninertial rotational diffusion. J. Chem. Phys. 2002;116:6422.
  • Tarasov VE. Fractional integro-differential equations for electromagnetic waves in dielectric media. Theor. Math. Phys. 2009;158:355–359.
  • Zubair M, Junaid Mughal M, Abbas Naqvi Q. Electromagnetic fields and waves in fractional dimensional space. In: Electromagnetic fields and waves in fractional dimensional space. Springer Briefs in Applied Sciences and Technology. New York (NY): Springer-Verlag Berlin Heidelberg; 2012. p. 7–16.
  • Rosales JJ, Guía M, Gómez JF, Tkach VI. Fractional electromagnetic wave. Discontinuity, Nonlinearity Comp. 2012;1:325–335.
  • Engheta N. On the role of fractional calculus in electromagnetic theory. Antenn. Propag. Mag. 1997;39:35–46.
  • Yépez-Martínez H, Reyes JM, Sosa IO. Analytical solutions to the fractional wave equation with variable dielectric function. Latin-Am. J. Phys. Edu. 2014;8:155–161.
  • Gómez Aguilar JF, Baleanu D. Fractional transmission line with losses. Z. Naturforsch. 2014;69a:1–8.
  • Baleanu D, Golmankhaneh AK, Golmankhaneh AK, Baleanu MC. Fractional electromagnetic equations using fractional forms. Int. J. Theor. Phys. 2009;48:3114–3123.
  • Tarasov Vasily E. Fractional vector calculus and fractional Maxwell’s equations. Ann. Phys. 2008;323:2756–2778.
  • Balankin AS, Mena B, Patiño J, Morales D. Electromagnetic fields in fractal continua. Phys. Lett. A. 2013;377:738–788.
  • Baleanu D, Golmankhaneh AK, Golmankhaneh AK. On electromagnetic field in fractional space. Nonlinear Anal.: Real World Appl. 2010;11:288–292.
  • Tarasov VE. Fractional dynamics: application of fractional calculus to dynamics of particles, fields and media. New York (NY): Springer, HEP; 2011.
  • Tarasov VE, Trujillo JJ. Fractional power-law spatial dispersion in electrodynamics. Ann. Phys. 2013;334:1–23.
  • Ortigueira MD, Rivero M, Trujillo JJ. From a generalised helmholtz decomposition theorem to fractional Maxwell equations. Commun. Nonlinear Sci. Numer. Simulat. 2015;22:1036–1049.
  • Gómez-Aguilar JF, Rosales-García JJ, Bernal-Alvarado JJ, Córdova-Fraga T, Guzmán-Cabrera R. Fractional mechanical oscillators. Rev. Mex. Fís. 2012;58:348–352.
  • Haubold HJ, Mathai AM, Saxena RK. Mittag-Leffler functions and their applications. J. Appl. Math. 2011;1:298628.
  • Nasrolahpour H. A note on fractional electrodynamics. Commun. Nonlinear Sci. Numer. Simulat. 2013;18:2589–2593.
  • Metzler R, Nonnenmacher TF. Space-and time-fractional diffusion and wave equations, fractional Fokker-Planck equations and physical motivation. Chem. Phys. 2002;284:67–90.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.