Document Type : Original Scientific Paper
Authors
Faculty of Physics, University of Kashan, Kashan, I. R. Iran
Abstract
Keywords
Main Subjects
[1] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
[2] M. Sadallah and S. I. Muslih, Solution of the equations of motion for Einstein’s field in fractional dimensional space-time, Int. J. Theor. Phys. 48 (2009) #3312, https://doi.org/10.1007/s10773-009-0172-6.
[3] F. H. Stillinger, Axiomatic basis for spaces with noninteger dimension, J. Math. Phys. 18 (1977) 1224-1234, https://doi.org/10.1063/1.523395.
[4] C. Palmer and P. N. Stavrinou, Equations of motion in a noninteger-dimensional space, J. Phys. A: Math. Gen. 37 (2004) #6987, https://doi.org/10.1088/0305-4470/37/27/009.
[5] M. Zubair, M. J. Mughal and Q. A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, Springer, Berlin, 2012.
[6] M. Zubair, M. J. Mughal, Q. A. Naqvi and A. A. Rizvi, Differential electromagnetic equations in fractional space, Prog. Electromagn. Res. 114 (2011) 255-269, https://doi.org/10.2528/PIER11011403.
[7] S. Khan and M. J. Mughal, General solution for TEM, TE and TM waves in fractional dimensional space and its application in rectangular waveguide filled with fractional space, J. Electromagn. Waves Appl. 27 (2013) 2298-2307,
https://doi.org/10.1080/09205071.2013.840543.
[8] S. Khan, A. Noor and M. J. Mughal, General solution for waveguide modes in fractional space, Prog. Electromagn. Res. 33 (2013) 105-120, https://doi.org/10.2528/PIERM13062807.
[9] S. Khan, F. M. A. Khan, Gulalai and A. Noor, General solution for electromagnetic wave propagation in cylindrical waveguide filled with fractional space, Waves Random Complex Media 33 (2023) 49-61, https://doi.org/10.1080/17455030.2021.1874076.
[10] M. Zubair, M. J. Mughal and Q. A. Naqvi, On electromagnetic wave propagation in fractional space, Nonlinear Anal. Real World Appl. 12 (2011) 2844-2850,https://doi.org/10.1016/j.nonrwa.2011.04.010.
[11] M. Zubair, M. J. Mughal and Q. A. Naqvi, The wave equation and general plane wave solutions in fractional space, Prog. Electromagn. Res. Lett. 19 (2010) 137-146, https://doi.org/10.2528/PIERL10102103.
[12] M. Zubair, M. J. Mughal and Q. A. Naqvi, An exact solution of the cylindrical wave equation for electromagnetic field in fractional dimensional space, Prog. Electromagn. Res. 114 (2011) 443-455, https://doi.org/10.2528/PIER11021508.
[13] M. Zubair, M. J. Mughal and Q. A. Naqvi, An exact solution of the spherical wave equation in d-dimensional fractional space, J. Electromagn. Waves Appl. 25 (2011) 1481-1491, https://doi.org/10.1163/156939311796351605.
[14] V. E. Tarasov, Electromagnetic fields on fractals, Mod. Phys. Lett. A 21 (2006) 1587-1600, https://doi.org/10.1142/S0217732306020974.
[15] M. Ostoja-Starzewski, Electromagnetism on anisotropic fractal media, Z. Angew. Math. Phys. 64 (2013) 381-390, https://doi.org/10.1007/s00033-012-0230-z.
[16] A. M. Attiya, Reflection and transmission of electromagnetic wave due to a quasi-fractional-space slab, Prog. Electromagn. Res. 24 (2011) 119-128, https://doi.org/10.2528/PIERL11051105.
[17] H. Asad, M. Zubair and M. J. Mughal, Reflection and transmission at dielectric-fractal interface, Prog. Electromagn. Res. 125 (2012) 543-558, https://doi.org/10.2528/PIER12012402.
[18] M. Omar and M. J. Mughal, Behavior of electromagnetic waves at dielectric fractal-fractal interface in fractional spaces, Prog. Electromagn. Res. 28 (2013) 229-244, https://doi.org/10.2528/PIERM12121903.
[19] D. Baleanu, A. K. Golmankhaneh and A. K. Golmankhaneh, On electromagnetic field in fractional space, Nonlinear Anal. Real World Appl. 11 (2010) 288-292, https://doi.org/10.1016/j.nonrwa.2008.10.058.
[20] S. I. Muslih and D. Baleanu, Fractional multipoles in fractional space, Nonlinear Anal. Real World Appl. 8 (2007) 198- 203, https://doi.org/10.1016/j.nonrwa.2005.07.001.
[21] A. Shreevastava, P. S. C. Rao and G. S. McGrath, Emergent self-similarity and scaling properties of fractal intra-urban heat islets for diverse global cities, Phys. Rev. E 100 (2019) #032142, https://doi.org/10.1103/PhysRevE.100.032142.
[22] M. Kompaniets and K. J. Wiese, Fractal dimension of critical curves in the O(n)-symmetric \phi^4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models, Phys. Rev. E 101 (2020) #012104, https://doi.org/10.1103/PhysRevE.101.012104.
[23] J. Zierenberg, N. Fricke, M. Marenz, F. P. Spitzner, V. Blavatska and W. Janke, Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects, Phys. Rev. E 96 (2017) #062125, https://doi.org/10.1103/PhysRevE.96.062125.
[24] O. Praud and H. L. Swinney, Fractal dimension and unscreened angles measured for radial viscous fingering, Phys. Rev. E 72 (2005) #011406, https://doi.org/10.1103/PhysRevE.72.011406.
[25] J. R. Westernacher-Schneider, Fractal dimension of turbulent black holes, Phys. Rev. D 96 (2017) #104054, https://doi.org/10.1103/PhysRevD.96.104054.
[26] C. Yeh, Elliptical dielectric waveguides, J. Appl. Phys. 33 (1962) 3235-3243, https://doi.org/10.1063/1.1931144.
[27] S. R. Rengarajan and J. E. Lewis, Dielectric loaded elliptical waveguides, IEEE Trans. Microw. Theory Tech. 28 (1980) 1085-1089, https://doi.org/10.1109/TMTT.1980.1130229.
[28] N. W. McLachlan, Theory and Application of Mathieu Functions, Dover, New York, 1964.
[29] P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw Hill, New York, 1953.
[30] M. Hortaçsu, Heun functions and some of their applications in physics, Adv. High Energy Phys. 2018 (2018) #8621573, https://doi.org/10.1155/2018/8621573
[31] A. Ronveaux, Heun’s Differential Equations, Oxford University Press, Oxford, UK, 1995.
[32] S. Y. Slavyanov and W. Lay, Special Functions: A Unified Theory Based on Singularities, Oxford University Press, Oxford, UK, 2000.
[33] C. A. Balanis, Advanced Engineering Electromagnetics, Wiley, New York, 1989.