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2018-06-13

The Use of the Fractional Derivatives Approach to Solve the Problem of Diffraction of a Cylindrical Wave on an Impedance Strip

Eldar I. Veliyev,

Dr. Eldar I. Veliyev

Information Institute of Istanbul Technical University

Turkey

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Kamil Karaçuha,

Mr. Kamil Karaçuha

Department of Electrical Engineering

Istanbul Technical University

Turkey

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Ertuğrul Karaçuha,

Dr. Ertuğrul Karaçuha

Information Institute of Istanbul Technical University

Turkey

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Osman Dur

Dr. Osman Dur

Information Institute of Istanbul Technical University

Turkey

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Progress In Electromagnetics Research Letters, Vol. 77, 19-25, 2018

doi:10.2528/PIERL18032202 | Google Scholar

Abstract

Earlier, we considered the use of the apparatus of fractional derivatives to solve the two-dimensional problem of diffraction of a plane wave on an impedance strip. We introduced the concept of a ``fractional strip''. A ``fractional strip'' is understood as a strip on the surface, which is subject to fractional boundary conditions (FBC). The problem under consideration on the basis of various methods has been studied quite well. As a rule, this problem is studied on the basis of numerical methods. The proposed approach, as will be shown below, makes it possible to obtain an analytical solution of the problem for values of fractional order v = 0.5 and for fractional values of the interval v∈[0,1], the general solution needs to be investigated numerically.

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Eldar I. Veliyev, Kamil Karaçuha, Ertuğrul Karaçuha, and Osman Dur, "The Use of the Fractional Derivatives Approach to Solve the Problem of Diffraction of a Cylindrical Wave on an Impedance Strip," Progress In Electromagnetics Research Letters, Vol. 77, 19-25, 2018.
doi:10.2528/PIERL18032202

References

1. Veliev, E. I., M. V. Ivakhnychenko, and T. M. Ahmedov, "Fractional boundary conditions in plane waves diffraction on a strip," Progress In Electromagnetics Research, Vol. 79, 443-462, 2008.
doi:10.2528/PIER07102406 Google Scholar

2. Ivakhnychenko, M. V., E. I. Veliev, and T. M. Ahmedov, "Scattering properties of the strip with fractional boundary conditions and comparison with the impedance strip," Progress In Electromagnetics Research C, Vol. 2, 189-205, 2008.
doi:10.2528/PIERC08031502 Google Scholar

3. Samko, S. G., A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, 1993.

4. Balanis, C. A., Advanced Engineering Electromagnetic, Wiley, 1989.

5. Veliev, E. and N. Engheta, "Generalization of Green’s Theorem with fractional differintegration," 2003 IEEE AP-S International Symposium & USNC/URSI National Radio Science Meeting, 2003. Google Scholar

6. Veliev, E. I., T.M. Ahmedov, and M. V. Ivakhnychenko, "Fractional Green’s function and fractional boundary conditions in diffraction of electromagnetic waves on plane screens," Azerbaijan Journal of Mathematics, Vol. 1, No. 1, January 2011. Google Scholar