Fractional electromagnetic waves in conducting media

References

• Oldham KB, Spanier J. The fractional calculus. New York (NY): Academic Press; 1974.
   Google Scholar
• Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. New York (NY): John Wiley; 1993.
   Google Scholar
• Li C, Zeng F. Numerical methods for fractional calculus. Boca Raton (FL): CRC Press; 2015.
   Google Scholar
• Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
   Google Scholar
• Dumitru B, Diethelm K, Scalas E, et al. Fractional calculus models and numerical methods. Series on complexity, nonlinearity and chaos. Singapore: World Scientific; 2012.
   Google Scholar
• Martin R, Quintana JJ, Ramos A, et al. Modeling of electrochemical double layer capacitors by means of fractional impedance. ASME Comput. Nonlinear Dyn. 2008;3:1–6.
   Google Scholar
• Gómez-Aguilar F, Alvarado-Méndez E. Description of the dynamics of charged particles in electric fields: an approach using fractional calculus. In: Advanced lasers. Netherlands: Springer; 2015. p. 147–158. doi:10.1007/978-94-017-9481-7.
   Google Scholar
• Gómez Aguilar JF, Miranda Hernández M. Space-time fractional diffusion-advection equation with caputo derivative. Abs. Appl. Anal. 2014;8:1–8. Article ID 283019.
   Google Scholar
• Diethelm K. The analysis of fractional differential equations an application-oriented exposition using differential operators of caputo type. NewYork (NY): Springer; 2010.
   Google Scholar
• Baleanu D, Golmankhaneh AK, Golmankhaneh Ali K, et al. Newtonian law with memory. Nonlinear Dyn. 2010;60:81–86.
   Web of Science ®Google Scholar
• Gómez-Aguilar JF, Baleanu D. Fractional transmission line with losses. Z. Naturforsch. 2014;69a:539–546. doi:10.5560/ZNA.2014-0049.
   Google Scholar
• Alireza K, Golmankhaneh VF, Baleanu D. Newtonian mechanics on fractals subset of real-line. Romanian Rep. Phys. 2013;65:84–93.
   Web of Science ®Google Scholar
• Golmankhaneh AK, Ali MY, Baleanu D. On the fractional hamilton and lagrange mechanics. Int. J. Theor. Phys. 2012;51:2909–2916.
   Web of Science ®Google Scholar
• Sami IM, Saddallah M, Baleanu D, et al. Lagrangian formulation of Maxwell’s field in fractional D dimensional space-time. Romanian J. Phys. 2010;55:659–663.
   Web of Science ®Google Scholar
• Engheta N. On fractional calculus and fractional multipoles in electromagnetism. IEEE Trans. Antennas Propag. 1996;44:554–566.
   Web of Science ®Google Scholar
• Hussain A, Faryad M, Naqvi QA. Fractional curl operator and fractional chiro-waveguide. J. Electromagn. Waves Appl. 2007;21:1119–1129.
   Web of Science ®Google Scholar
• Faryad M, Naqvi QA. Progress in electromagnetic research. PIER. 2007;75:383–396.
   Web of Science ®Google Scholar
• Tarasov VE. Anisotropic fractal media by vector calculus in non-integer dimensional space. J. Math. Phys. 2014;55:083510.
   Web of Science ®Google Scholar
• Zubair M, Mughal MJ, Naqvi QA. On electromagnetic wave propagation in fractional space. Nonlinear Anal.: Real World Appl. 2011;12:2844–2850.
   Web of Science ®Google Scholar
• Gómez-Aguilar JF, Yépez-Martínez H, Escobar-Jiménez RF, et al. Universal character of the fractional space-time electromagnetic waves in dielectric media. J. Electromagn. Waves Appl. 2015;29:727–740.
   Web of Science ®Google Scholar
• Van Groesen E, Mainardi F. Energy propagation in dissipative systems. Part I: centrovelocity for linear systems. Wave Motion. 1989;11:201–209.
   Web of Science ®Google Scholar
• Van Groesen E, Mainardi F. Balance laws and centrovelocity in dissipative systems. J. Math. Phys. 1990;31:2136–2140.
   Web of Science ®Google Scholar
• Luchko Y. Fractional wave equation and damped waves. J. Math. Phys. 2013;54:031505.
   Web of Science ®Google Scholar
• Ma Y, Zhang F, Li C. The asymptotics of the solutions to the anomalous diffusion equations. Comput. Math. Appl. 2013;66:682–692.
   Web of Science ®Google Scholar
• Can L, Wei-Hua D, Xiao-Qin S. Exact solutions and their asymptotic behaviors for the averaged generalized fractional elastic models. Commun. Theor. Phys. 2014;62:443–453.
   Web of Science ®Google Scholar
• Agrawal OP. Solution for a fractional diffusion-wave equation defined in a bounded domain. Nonlinear Dyn. 2002;29:145–155.
   Web of Science ®Google Scholar
• Engheta N. On the role of fractional calculus in electromagnetic theory. Antennas Propag. Mag. 1997;39:35–46.
   Web of Science ®Google Scholar
• Balankin AS, Mena B, Patiño J, et al. Electromagnetic fields in fractal continua. Phys. Lett. A. 2013;377:738–788.
   Google Scholar
• Tarasov VE, Trujillo JJ. Fractional power-law spatial dispersion in electrodynamics. Ann. Phys. 2013;334:1–23.
   Web of Science ®Google Scholar
• Tarasov VE. Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. New York (NY): Springer Science & Business Media; 2011.
   Google Scholar
• Yépez-Martínez H, Reyes JM, Sosa IO. Analytical solutions to the fractional wave equation with variable dielectric function. Lat. Am. J. Phys. Edu. 2014;8:155–161.
   Google Scholar
• Baleanu D, Golmankhaneh Ali K, Golmankhaneh AK, et al. Fractional electromagnetic equations using fractional forms. Int. J. Theor. Phys. 2009;48:3114–3123.
   Web of Science ®Google Scholar
• Tarasov VE. Fractional integro-differential equations for electromagnetic waves in dielectric media. Theor. Math. Phys. 2009;158:355–359.
   Web of Science ®Google Scholar
• Naqvi A, Ahmed S, Naqvi QA. Perfect electromagnetic conductor and fractional dual interface placed in a chiral nihility medium. J. Electromag. Waves Appl. 2010;24:1991–1999.
   Web of Science ®Google Scholar
• Naqvi A, Hussain A, Naqvi QA. Waves in fractional dual planar waveguides containing chiral nihility metamaterial. J. Electromag. Waves Appl. 2010;24:1575–1586.
   Web of Science ®Google Scholar
• Ezzat MA, El-Karamany AS, El-Bary AA. A novel magneto-thermoelasticity theory with memory-dependent derivative. J. Electromag. Waves Appl. 2015;29:1–14.
   Web of Science ®Google Scholar
• Tarasov VE. Electromagnetic waves in non-integer dimensional spaces and fractals. Chaos Solitons Fractals. 2015;81:38–42.
   Web of Science ®Google Scholar
• Nasrolahpour H. A note on fractional electrodynamics. Commun. Nonlinear Sci. Numer. Simul. 2013;18:2589–2593.
   Web of Science ®Google Scholar
• Gómez-Aguilar JF, Razo-Hernández R, Granados-Lieberman D. A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response. Rev. Mex. Fis. 2014;60:32–38.
   Web of Science ®Google Scholar
• Diethelm K, Ford NJ, Freed AD, et al. Algorithms for the fractional calculus: a selection of numerical methods. Comp. Methods Appl. Mech. Eng. 2005;194:743–773.
   Web of Science ®Google Scholar
• Tarasov VE. Fractional vector calculus and fractional Maxwell’s equations. Ann. Phys. 2008;323:2756–2778.
   Web of Science ®Google Scholar