Fractional curl operator in radiation problems

Ivakhnychenko, M.V.; Велиев, Е. И.

doi:10.1109/mmet.2004.1396991

Cited by 10 publications

(5 citation statements)

References 2 publications

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“…Both approaches have been compared with the multifractional framework in [44,62]. Fractional calculus has been more extensively employed to describe Maxwell electrodynamics with fractal charge distributions [63,64] or in fractal turbulent media [65,66] (where a fractional integration measure makes its appearance), or in dielectric media and various problems [67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83] (where effective electromagnetic equations sport fractional derivatives). These scenarios are neither associated with intrinsically anomalous spacetimes (except as a heuristic motivation for [79,82]) nor formulated in a field-theory context.…”

Section: Electromagnetism and Fermions In Multifractional Field mentioning

confidence: 99%

Varying electric charge in multiscale spacetimes

2014

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We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying-coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multifractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion.

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Section: Electromagnetism and Fermions In Multifractional Field mentioning

confidence: 99%

Varying electric charge in multiscale spacetimes

2014

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“…The current density has zero values outside of the strip. The fractional Green's function G ν (x) has the form given as follows [5][6][7]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Its spectral representation is given in (8). By the spectral representation, the Hankel function can be written as the summation of plane waves [5][6][7]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Using the properties of the fractional derivative approach, the intermediate stages of fields or sources between two canonical states can be described [1][2][3][4][5]. Since then, several studies have been performed on scattering problems [6][7][8][9][10]. The integral boundary condition, which corresponds to an intermediate boundary condition between Dirichlet and Neumann boundary conditions, is used in order to explain the scattering properties of different geometries.…”

Section: Introductionmentioning

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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“…[3][4][5][6][7][8][9][10][11][12][13][14][15]. Valuable contributions on this topic are given by other authors [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Fractional Rectangular Cavity Resonator

Maab¹,

Naqvi²

2008

PIER B

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Abstract-Fractional curl operator has been used to derive solutions to the Maxwell equations for fractional rectangular cavity resonator. These solutions to the Maxwell equations may be regarded as fractional dual solutions. Behavior of field lines and surface current density in fractional cavity resonator have been investigated with respect to the fractional parameter. Fractional parameter describes the order of fractional curl operator.

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Fractional curl operator in radiation problems

Cited by 10 publications

References 2 publications

Varying electric charge in multiscale spacetimes

Varying electric charge in multiscale spacetimes

Plane wave diffraction by strip with an integral boundary condition

Fractional Rectangular Cavity Resonator

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