Maxwell's equations and electromagnetic Lagrangian density in fractional form

Jaradat, Emad K.; Hijjawi, R. S.; Khalifeh, J. M.

doi:10.1063/1.3670375

Cited by 13 publications

(5 citation statements)

References 24 publications

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“…Taking into consideration that´R 3 g(−x) d 3 x =´R 3 g(x) d 3 x, e + (k) = e(k) and e − (k) = e(−k), one can write (71) as follows:…”

Section: Plane-wave Propagationmentioning

confidence: 99%

“…Recently, the problem of electrodynamics of fractional order (FO) has been introduced in the literature. Between various approaches, one can notice the generalizations of Maxwell's equations involving spatial and temporal FO derivatives [1][2][3][4][5], only spatial derivatives [6][7][8], and only temporal FO derivatives [9][10][11][12]. Such generalizations of Maxwell's equations employ FO derivatives in order to describe the dynamics of electromagnetic systems with memory and energy dissipation [13].…”

Section: Introductionmentioning

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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“…Taking into consideration that´R 3 g(−x) d 3 x =´R 3 g(x) d 3 x, e + (k) = e(k) and e − (k) = e(−k), one can write (71) as follows:…”

Section: Plane-wave Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Stefański

Gulgowski

2021

Entropy

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“…Fractional-order modeling can more accurately reflect some complex dynamic characteristics in the fields of natural science and engineering. In the field of electrical engineering, research work using fractional calculus has demonstrated some Interesting results, such as the fractional-order model of permanent magnet synchronous motor [7,8], the fractionalorder model of a power system [9], the ferromagnetic of a fractional-order power system's ferromagnetic resonant chaotic model [10], a fractional RLC circuit model [11], a fractional filter [12], a fractional DC-DC converter [13], a fractional Chua's circuit [14], fractional Maxwell equations for electromagnetic field [15], etc. In recent years, the control of fractional-order chaotic power systems has drawn the attention of experts [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation of Fractional-Order Chaotic Power System Based on Lens Imaging Learning Strategy State Transition Algorithm

Fan

2023

IEEE Access

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：Parameter identification of fractional-order chaotic power systems is a multidimensional optimization problem that plays a decisive role in the synchronization and control of fractional-order chaotic power systems. In this paper, a state transition algorithm based on the lens imaging learning strategy is proposed for parameter identification of fractional-order chaotic power systems. Taking a fractional-order six-dimensional chaotic power system mathematical model as an example, the mathematical model and chaotic state are analyzed. First, the Tent chaotic mapping is used to initialize the population, thus increasing population diversity. The randomness and ergodicity of the Tent chaotic sequence are used to enhance the global searching ability of the algorithm. Second, a maturity index is employed to determine population maturity. The lens imaging learning strategy is used to suppress the premature convergence of the state transition algorithm effectively and help the population jump out of local optima. Finally, the improved state transition algorithm is used to identify the parameters of the fractional-order six-dimensional chaotic power system model. The proposed improved state transition algorithm shows high estimation accuracy and convergence speed, and is superior to the traditional state transition and particle swarm optimization algorithms. The simulation results show that the parameters of the fractional-order chaotic power system are identified accurately even in the presence of white noise, demonstrating the strong robustness and versatility of the proposed algorithm.

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“…There has been a surge of research in fractional calculus, leading to its application in physics, engineering, and related areas [13][14][15][16]. The Maxwell equations have been expressed in fractional form [17][18][19], as have those in quantum mechanics, including the fractional Schrödinger equation [20,21] and the fractional Dirac equation [22]. These advancements demonstrate the versatility of fractional calculus in describing a wide range of physical systems.…”

Section: Introductionmentioning

confidence: 99%

Composite Fermions QED Lagrangian Density in Fractional Formulation

Al-Oqali

2023

East Eur. J. Phys.

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Quantum electrodynamics (QED) is a highly precise and successful theory that describes the interaction between electrically charged particles and electromagnetic radiation. It is an integral part of the Standard Model of particle physics and provides a theoretical basis for explaining a wide range of physical phenomena, including the behavior of atoms, molecules, and materials. In this work, the Lagrangian density of Composite Fermions in QED has been expressed in a fractional form using the Riemann‑Liouville fractional derivative. The fractional Euler-Lagrange and fractional Hamiltonian equations, derived from the fractional form of the Lagrangian density, were also obtained. When α is set to 1, the conventional mathematical equations are restored.

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Maxwell's equations and electromagnetic Lagrangian density in fractional form

Cited by 13 publications

References 24 publications

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

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

Parameter Estimation of Fractional-Order Chaotic Power System Based on Lens Imaging Learning Strategy State Transition Algorithm

Composite Fermions QED Lagrangian Density in Fractional Formulation

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