Evolution of a current in a resistor

Obeidat, Abdalla; Gharaibeh, Maen; Al-Ali, Manal; Rousan, Akram

doi:10.2478/s13540-011-0015-7

Cited by 10 publications

(9 citation statements)

References 12 publications

(8 reference statements)

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“…Consider the electrical series circuit RC with R = 10 O, C = 0:1 F, and V 0 = 10 V. Figure 1(a)-(d) shows numerical simulations for the voltage across the capacitor considering unit step source with bi-order operator, equation (16) and unit step source with ABC operator, equation (24) and periodic source with bi-order operator (27) and periodic source with ABC operator, equation (32), for different particular cases of a and b.…”

Section: Rl Electrical Circuitmentioning

confidence: 99%

Electrical circuits RC and RL involving fractional operators with bi-order

Gómez-Aguilar

Escobar-Jiménez

Olivares-Peregrino

et al. 2017

Advances in Mechanical Engineering

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This article describes electrical series circuits RC and RL using the concept of derivative with two fractional orders a and b in Liouville-Caputo sense. The fractional equations consider derivatives in the range of a, b 2 (0; 1. Numerical solutions are presented considering different source terms introduced in the fractional equation. This new approach considers electrical elements with two different properties. In addition, we prove that if a = 0, the fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense is recovered, and when b = 0, the Liouville-Caputo fractional derivative is recovered.

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Section: Rl Electrical Circuitmentioning

confidence: 99%

Electrical circuits RC and RL involving fractional operators with bi-order

Gómez-Aguilar

Escobar-Jiménez

Olivares-Peregrino

et al. 2017

Advances in Mechanical Engineering

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“…[11][12][13][14][15]. The use of fractional order operators allows us to generalize the propagation of electrical signals in devices, circuits, and networks [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On the Possibility of the Jerk Derivative in Electrical Circuits

Gómez-Aguilar

Rosales

Escobar-Jiménez

et al. 2016

Advances in Mathematical Physics

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A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics. Some mechanical and acoustic systems can be interpreted as jerky dynamics. In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ. We consider fractional LC and RL electrical circuits with 1⩽γ<2 for different source terms. The LC circuit has a frequency ω dependent on the order of the fractional differential equation γ, since it is defined as ω(γ)=ω0γγ1-γ, where ω0 is the fundamental frequency. For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.

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“…The behavior of this new hybrid circuit without sources has been analyzed [8]. In the work of [9], the simple current sourcewire circuit has been studied fractionally using direct and alternating current source. It was shown that the wire acquires an inducting behavior as the current is initiated in it and gradually recovers its resisting behavior.…”

Section: Introductionmentioning

confidence: 99%