Fractional Operators Approach in Electromagnetic Wave Reflection Problems

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

doi:10.1163/156939307781891012

Cited by 20 publications

(5 citation statements)

References 14 publications

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“…The applications of fractional curl operator was further extended by Naqvi et al [2], they discussed the behavior of fractional dual solution in an unbounded chiral medium. Veliev and Engheta [3] and Ivakhnychenko et al [4] utilized the fractional curl operator to a fixed solution and obtained the fractional fields that represent the solution of reflection problem from anisotropic surface impedance. Hussain and Naqvi [5], introduction the idea of fractional nonsymmetric transmission line.…”

Section: Introductionmentioning

confidence: 99%

Fractional Surface Waveguide

Maab¹,

Naqvi²

2008

PIER C

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Fractional curl operator has been utilized to study the fractional order surface waveguides. Fractional order surface waveguides may be regarded as intermediate step of two surface waveguides which are related through the principle of duality. Fractional eigenvalue equations are examined at the interface between dielectric medium and free space, for various values of fractional order parameter result in different fractional surface wave modes.

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Section: Introductionmentioning

confidence: 99%

Fractional Surface Waveguide

Maab¹,

Naqvi²

2008

PIER C

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“…Let us study the problem (32) when the boundary conditions are homogeneous, i.e., consider the problem:…”

Section: The Neumann Problemmentioning

confidence: 99%

“…Applications of the boundary value problems with boundary operators of fractionalorder for elliptic equations were given in [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions

2021

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A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary operator having a derivative of the Hadamard-type. First, transformations of the involution type were considered. The properties of the matrices of these transformations were investigated. As applications of the considered transformations, the questions about the solvability of a boundary value problem for a nonlocal biharmonic equation were studied. Modified Hadamard derivatives were considered as the boundary operator. The considered problems covered the Dirichlet and Neumann-type boundary conditions. Theorems on the existence and uniqueness of solutions to the studied problems were proven.

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“…In [6], the fractionalization of the duality principle in electrodynamics is proposed, making use of the FO curl operator. This approach can be applied to solve some reflection [17,18] and diffraction [19] problems. Afterwards, in [20], the FO curl operator is proven to be useful for the analysis of the transmission of electromagnetic waves through a slab of reciprocal chiral medium.…”

Section: Introductionmentioning

confidence: 99%

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Stefański

Gulgowski

2021

Entropy

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In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

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Fractional Operators Approach in Electromagnetic Wave Reflection Problems

Cited by 20 publications

References 14 publications

Fractional Surface Waveguide

Fractional Surface Waveguide

On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

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