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2010-12-13
The Wave Equation and General Plane Wave Solutions in Fractional Space
By
Progress In Electromagnetics Research Letters, Vol. 19, 137-146, 2010
Abstract
This work presents the analytical solution of vector wave equation in fractional space. General plane wave solution to the wave equation for fields in source-free and lossless media is obtained in fractional space. The obtained solution is a generalization of wave equation from integer dimensional space to a non-integer dimensional space. The classical results are recovered when integer-dimensional space is considered.
Citation
Muhammad Zubair, Muhammad Junaid Mughal, and Qaisar Naqvi, "The Wave Equation and General Plane Wave Solutions in Fractional Space," Progress In Electromagnetics Research Letters, Vol. 19, 137-146, 2010.
doi:10.2528/PIERL10102103
References

1. Stillinger, F. H., "Axiomatic basis for spaces with noninteger dimension," J. Math. Phys., Vol. 18, No. 6, 1224-1234, 1977.
doi:10.1063/1.523395

2. He, X., "Anisotropy and isotropy: A model of fraction-dimensional space," Solid State Commun., Vol. 75, 111-114, 1990.
doi:10.1016/0038-1098(90)90352-C

3. Muslih, S. and D. Baleanu, "Fractional multipoles in fractional space," Nonlinear Analysis: Real World Applications, Vol. 8, 198-203, 2007.
doi:10.1016/j.nonrwa.2005.07.001

4. Baleanu, D., A. K. Golmankhaneh, and A. K. Golmankhaneh, "On electromagnetic field in fractional space," Nonlinear Analysis: Real World Applications, Vol. 11, No. 1, 288-292, 2010.
doi:10.1016/j.nonrwa.2008.10.058

5. Tarasov, V. E., "Electromagnetic fields on fractals," Modern Phys. Lett. A, Vol. 21, No. 20, 1587-1600, 2006.
doi:10.1142/S0217732306020974

6. Palmer, C. and P. N. Stavrinou, "Equations of motion in a noninteger-dimension space," J. Phys. A, Vol. 37, 6987-7003, 2004.
doi:10.1088/0305-4470/37/27/009

7. Engheta, N., "Fractional curl operator in electromagnetics," Microwave Opt. Tech. Lett., Vol. 17, 86-91, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E

8. Naqvi, Q. A. and A. A. Rizvi, "Fractional dual solutions and corresponding sources," Progress In Electromagnetics Research, Vol. 25, 223-238, 2000.
doi:10.2528/PIER99051801

9. Engheta, N., "Use of fractional integration to propose some `fractional' solutions for the scalar Helmholtz equation," Progress In Electromagnetics Research, Vol. 12, 107-132, 1996.

10. Hussain, A., S. Ishfaq, and Q. A. Naqvi, "Fractional curl operator and fractional waveguides," Progress In Electromagnetics Research, Vol. 63, 319-335, 2006.
doi:10.2528/PIER06060604

11. Willson, K. G., "Quantum field-theory, models in less than 4 dimensions," Phys. Rev. D, Vol. 7, No. 10, 2911-2926, 1973.
doi:10.1103/PhysRevD.7.2911

12. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York, 1989.

13. Polyanin, A. D. and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2 Ed., CRC Press, Boca Raton, New York, 2003.

14. Jeffrey, A., Handbook of Mathematical Formulas and Integrals, Academic Press, 1995.

15. Wang, Z.-S. and B.-W. Lu, "The scattering of electromagnetic waves in fractal media," Waves in Random and Complex Media, Vol. 4, No. 1, 97-103, 1994.

16. Hussain, A. and Q. A. Naqvic, "Fractional rectangular impedance waveguide," Progress In Electromagnetics Research, Vol. 96, 101-116, 2009.
doi:10.2528/PIER09060801

17. Naqvi, Q. A., "Fractional dual interface in chiral nihility medium," Progress In Electromagnetics Research Letters, Vol. 8, 135-142, 2009.
doi:10.2528/PIERL09032405