Fractional Operators Approach and Fractional Boundary Conditions

Велиев, Е. И.; Ahmedov, T. M.; Ivakhnychenko, Maksym

doi:10.5772/16300

Cited by 6 publications

(20 citation statements)

References 21 publications

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“…Throughout the study, Meixner's edge conditions need to be taken into account for x → 0 as including the weighting ς ν− 1 2 in Eq. (9) [7]. This representation guarantees thatf 1−ν satisfies the edge conditions.…”

Section: The Formulation Of the Problemmentioning

confidence: 93%

“…The first studies related to the fractional approach for the electromagnetic theory and its applications are investigated by Engheta [4][5][6]. Then, Veliyev et al developed the idea for the boundary condition which is called the fractional boundary condition (FBC) [7]. The fractional boundary condition used in previous works [8][9][10][11] explains a new material property (Perfect Electric Conducting (PEC), Perfect Magnetic Conducting (PMC) or in between).…”

Section: Introductionmentioning

confidence: 99%

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The Diffraction by the Half-Plane With the Fractional Boundary Condition

Veliyev¹,

Tabatadze²,

Karaçuha³

et al. 2020

PIER M

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The electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions is considered in this article. The theoretical part is given based on that the near field, pointing vector, and energy density distribution are calculated for different values of the fractional order. The results are compared with classical cases for marginal values of the fractional order. Interesting results are obtained for fractional orders between marginal values. Results are analyzed.

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Section: The Formulation Of the Problemmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

The Diffraction by the Half-Plane With the Fractional Boundary Condition

Veliyev¹,

Tabatadze²,

Karaçuha³

et al. 2020

PIER M

View full text Add to dashboard Cite

show abstract

“…In order to find the scattered electric field, the total electric field needs to satisfy the boundary condition on the surface of the strip [7][8][9][10]. Here, the boundary condition is the fractional boundary condition and the mathematical expression is given as:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The other important physical characteristic of the strip is the impedance. The normalized impedance of the strip can be found as η ν = − i sinθ tan( πν 2 ) [7,9]. Then the fractional order for the specific impedance value of the surface can be found by using (22).…”

Section: Physical Characteristics Of the Electric Fieldmentioning

confidence: 99%

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Plane wave diffraction by strip with an integral boundary condition

Karaçuha¹,

Tabatadze²,

Велиев³

2020

Turk J Elec Eng & Comp Sci

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In this article, a new solution method is proposed for plane wave diffraction by a strip. On the surface of the strip, an integral boundary condition is used. The impedance of the strip is investigated. The theoretical and numerical analyses show that there is a relation between the complex-valued fractional order of the integral boundary condition and properties of the material such as the impedance. As a further study, the total radar cross-section is investigated using the proposed method.

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Electromagnetic scattering of H‐polarised cylindrical wave by a double‐sided impedance circular strip

Tabatadze,

Alperen,

Karaçuha

2023

IET Microwaves Antenna & Prop

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The authors investigate electromagnetic scattering by a circular strip with impedance boundary conditions in detail. The excitation is obtained by the H‐polarised line source and the impedance boundary condition with different impedance values on each surface of the circular strip is imposed. Electromagnetic scattering from circular strips is formulated employing an integral equation approach including the orthogonal polynomials while expressing the current densities on inner and outer surfaces. To consider the edge condition, the current density on the scatterer is expressed in terms of Gegenbauer polynomials with the weighting function. Unlike the previous studies, the authors investigate the behaviour of the EM field regarding the location of the cylinder source, the size of the aperture and the different impedance values. The convergence of the proposed approach, which is one of the analytical–numerical methods, is investigated for different impedance values; considering the results, resonators with impedance surfaces of certain complex values and certain locations of the cylinder source perform better than the known PEC and PMC resonators for some specific resonance cases. An effective analytical–numerical approach is proposed for such geometry with the impedance boundary condition. An extensive analysis and comparison with other methods are provided. The limit cases of the impedance boundary condition (Dirichlet and Neumann boundary conditions) are validated.

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Fractional Operators Approach and Fractional Boundary Conditions

Cited by 6 publications

References 21 publications

The Diffraction by the Half-Plane With the Fractional Boundary Condition

The Diffraction by the Half-Plane With the Fractional Boundary Condition

Plane wave diffraction by strip with an integral boundary condition

Electromagnetic scattering of H‐polarised cylindrical wave by a double‐sided impedance circular strip

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