Signal propagation in electromagnetic media described by fractional-order models

Stefański, Tomasz P.; Gulgowski, Jacek

doi:10.1016/j.cnsns.2019.105029

Cited by 36 publications

(29 citation statements)

References 44 publications

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“…for (s) ≥ 0. As discussed in [34] (see (5) therein), this limitation stems from the memory of derivative, which covers the entire interval (−∞, t). Therefore, allowing for (s) < 0 would lead to divergent integrals.…”

Section: Fo Calculusmentioning

confidence: 99%

“…where E and H are, respectively, the electric-and magnetic-field intensities, D and B are, respectively, the electric-and magnetic-flux densities, J and M are, respectively, the electricand magnetic-current densities, and ρ e and ρ m are, respectively, the electric-and magneticcharge densities. We assume the constitutive relations for the medium described by FOM in the following form [34,36]:…”

Section: Rs Vectormentioning

confidence: 99%

“…For a vacuum, we assume that the permittivity and permeability are respectively denoted by 0 and µ 0 . Comparing to the settings considered before [34], we assume the same FO of all the time derivatives in ( 23)- (26) in order to formulate TF Maxwell's equations based on the RS vector. In our considerations, we assume that 1 2 ≤ β = γ ≤ 1.…”

Section: Rs Vectormentioning

confidence: 99%

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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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Section: Fo Calculusmentioning

confidence: 99%

Section: Rs Vectormentioning

confidence: 99%

Section: Rs Vectormentioning

confidence: 99%

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

Stefański

Gulgowski

2021

Entropy

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“…as well, having amplitudes u C0 and i 0 and phase angles φ C and φ i , due to linearity of fractional RC circuits' governing equations ( 23) and (24). Note, the quantities having physical meaning in (38) and (39) are Re E, Re u C , and Re i.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Review of fractional order element's characteristics, along with their dierent realizations and their application in modeling various phenomena is given in [36]. Constitutive models of electric elements may even be derived from modeling the interaction of the electro-magnetic eld with material, see [25,39].…”

Section: Introductionmentioning

confidence: 99%

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

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Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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Sliding‐mode boundary control for perturbed time fractional parabolic systems with spatially varying coefficients using backstepping

Chen

Zhuang

2022

Asian Journal of Control

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In this paper, we consider the boundary stabilization of an uncertain time fractional parabolic systems governed by time fractional parabolic partial differential equations (PDEs) with a boundary input disturbance and spatially varying coefficients (nonconstant coefficients) using a fractional‐order sliding‐mode controller. For this, the backstepping approach is used to transform an original system into a target system with a new manipulable input and perturbation. Then, the fractional‐order sliding‐mode algorithm is employed to design this new discontinuous boundary input to achieve the asymptotical stabilization of the target system (and, therefore, of the original system as well) by the fractional Lyapunov method. Apart from this, the well‐posedness of the fractional parabolic system is analyzed theoretically. Fractional‐order numerical simulations are provided to validate the developed technique.

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Signal propagation in electromagnetic media described by fractional-order models

Cited by 36 publications

References 44 publications

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

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

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Sliding‐mode boundary control for perturbed time fractional parabolic systems with spatially varying coefficients using backstepping

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Signal propagation in electromagnetic media described by fractional-order models

Cited by 36 publications

References 44 publications

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

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

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

Sliding‐mode boundary control for perturbed time fractional parabolic systems with spatially varying coefficients using backstepping

Contact Info

Product

Resources

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Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits