Electromagnetic Green’s function for fractional space

References

• Mandelbrot , B . 1983 . The fractal geometry of nature , New York , NY : W.H. Freeman .
   Google Scholar
• Palmer , C and Stavrinou , PN . 2004 . Equations of motion in a noninteger-dimension space . Journal of Physics A , 37 : 6987 – 7003 .
   Google Scholar
• Stillinger , FH . 1977 . Axiomatic basis for spaces with non-integer dimension . Journal of Mathematics and Physics , 18 ( 6 ) : 1224 – 1234 .
   Web of Science ®Google Scholar
• Tarasov , VE . 2005 . Continuous medium model for fractal media . Physics Letter A , 336 : 2 – 3 .
   Google Scholar
• Tarasov , VE . 2006 . Electromagnetic fields on fractals . Modern Physics Letter A , 21 ( 20 ) : 1587 – 1600 .
   Web of Science ®Google Scholar
• Muslih , SI and Agrawal , OP . 2009 . A scaling method and its applications to problems in fractional dimensional space . Journal of Mathematical Physics , 50 ( 12 ) : 123501 – 123511 .
   Web of Science ®Google Scholar
• Wang , Z-S and Lu , B-W . 1994 . The scattering of electromagnetic waves in fractal media . Waves in Random and Complex Media , 4 ( 1 ) : 97 – 103 .
   Google Scholar
• Engheta , N . 1998 . Fractional curl operator in electromagnetics . Microwave and Optical Technology Letters , 17 : 86 – 91 .
   Web of Science ®Google Scholar
• Naqvi , A , Hussain , A and Naqvi , QA . 2010 . Waves in fractional dual planar waveguides containing chiral nihility metamaterial . Journal of Electromagnetic Waves and Applications , 24 ( 11–12 ) : 1575 – 1586 .
   Web of Science ®Google Scholar
• Naqvi , A , Ahmed , S and Naqvi , QA . 2010 . Perfect electromagnetic conductor and fractional dual interface placed in a chiral nihility medium . Journal of Electromagnetic Waves and Applications , 24 ( 14–15 ) : 1991 – 1999 .
   Web of Science ®Google Scholar
• Zubair , M , Mughal , MJ , Naqvi , QA and Rizvi , AA . 2011 . Differential electromagnetic equations in fractional space . Progress in Electromagnetic Research , 114 : 255 – 269 .
   Web of Science ®Google Scholar
• Zubair , M , Mughal , MJ and Naqvi , QA . 2011 . On electromagnetic wave propagation in fractional space . Nonlinear Analysis B: Real World Applications , 12 ( 5 ) : 2844 – 2850 .
   Web of Science ®Google Scholar
• Zubair , M , Mughal , MJ and Naqvi , QA . 2010 . The wave equation and general plane wave solutions in fractional space . Progress in Electromagnetics Research Letters , 19 : 137 – 146 .
   Google Scholar
• Zubair , M , Mughal , MJ and Naqvi , QA . 2011 . An exact solution of the cylindrical wave equation for electromagnetic field in fractional dimensional space . Progress in Electromagnetics Research , 114 : 443 – 455 .
   Web of Science ®Google Scholar
• Zubair , M , Mughal , MJ and Naqvi , QA . 2011 . An exact solution of spherical wave in D-dimensional fractional space . Journal of Electromagnetic Waves and Applications , 25 ( 10 ) : 1481 – 1491 .
   Web of Science ®Google Scholar
• Zubair M, Mughal MJ, Naqvi QA, Electromagnetic fields and waves in fractional dimensional space, Springer Briefs in Applied Sciences and Technology, 2012, ISBN 978-3-642-25357-7, DOI: 10.1007/978-3-642-25358-4.
   Google Scholar
• Mughal MJ, Zubair M. Fractional space solutions of antenna radiation problems: an application to hertzian dipole, IEEE 19th Conference on Signal Processing and Communications Applications (SIU), 62–65, April 20–22, 2011.
   Google Scholar
• Teng , HT , Ewe , H-T and Tan , SL . 2010 . Multifractal dimension and its geometrical terrain properties for classification of multi-band multi-polarised SAR image . Progress in Electromagnetics Research , 104 : 221 – 237 .
   Web of Science ®Google Scholar
• Anguera , J , Daniel , JP , Borja , C , Mumbru , J , Puente , C , Leduc , T , Sayegrih , K and Van Roy , P . 2010 . Metallized foams for antenna design: application to fractal-shaped sierpinski-carpet monopole . Progress in Electromagnetics Research , 104 : 239 – 251 .
   Web of Science ®Google Scholar
• Siakavara , K . 2010 . Novel fractal antenna arrays for satellite networks: circular ring sierpinski carpet arrays optimized by genetic algorithms . Progress in Electromagnetics Research , 103 : 115 – 138 .
   Web of Science ®Google Scholar
• Yildirim , A and Koak , H . 2012 . A more approximate Green’s function for the electric field vector with anisotropic properties . Journal of Electromagnetic Waves and Applications , 26 ( 1 ) : 24 – 33 .
   Google Scholar
• Gustafsson , M . 2010 . Accurate and efficient evaluation of modal Green’s functions . Journal of Electromagnetic Waves and Applications , 24 ( 10 ) : 1291 – 1301 .
   Web of Science ®Google Scholar
• Jarchi , S , Rashed-Mohassel , J and Faraji-Dana , R . 2010 . Analysis of microstrip dipole antennas on a layered metamaterial substrate . Journal of Electromagnetic Waves and Applications , 24 ( 5–6 ) : 755 – 764 .
   Web of Science ®Google Scholar
• Sun , CH , Chiu , CC and Li , CL . 2010 Aug . Time-domain inverse scattering of a two-dimensional metallic cylinder in slab medium using asynchronous particle swarm optimization . Progress in Electromagnetic Research M , 14 : 85 – 100 .
   Google Scholar
• Kurrant , DJ and Fear , EC . 2012 . Extraction of internal spatial features of inhomogeneous dielectric objects using near-field reflection data . Progress in Electromagnetic Research , 122 : 197 – 221 .
   Google Scholar
• Chen , RP and Raymond Ooi , CH . 2011 . Evolution and collapse of a Lorentz beam in Kerr medium . Progress in Electromagnetics Research , 121 : 39 – 52 .
   Google Scholar
• Attiya , AM . 2011 . Reflection and transmission of electromagnetic wave due to a quasi-fractional space slab . Progress in Electromagnetics Research Letters , 24 : 119 – 128 .
   Google Scholar
• Balanis , CA . 1989 . Advanced engineering electromagnetics , New York , NY : Wiley .
   Google Scholar