Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

Gómez-Aguilar, J. F.; Morales‐Delgado, V. F.; Taneco-Hernández, M.A.; Băleanu, Dumitru; Escobar-Jiménez, R.F.; Qurashi, Maysaa Mohamed Al

doi:10.3390/e18080402

Cited by 99 publications

(56 citation statements)

References 28 publications

(35 reference statements)

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“…-for selected transient problems, the solutions can be compared with results obtained through the evaluation of analytical solutions based on the Mittag-Leffler function [18,22,23,34]; -steady-state linear AC problems solved with the newly designed numerical methods can be compared with solutions obtained through the application of complex numbers.…”

Section: Motivationmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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This paper discusses the ability to obtain periodic steady-state solutions for fractional nonlinear circuit problems. For a class of nonlinear problems with fractional derivatives (based on the Caputo or Riemann-Liouville definitions), a methodology is proposed to derive equations representing the dependencies between the harmonics of the sought variables. Two approaches are considered for how to address the apparent nonlinear dependencies: one based on symbolic computation and the other a numerical approach based on the analysis of time functions. An example problem with fractional and nonlinear elements is presented to illustrate the usefulness of the proposed methodology. Two error criteria are introduced to verify the accuracy of the obtained results. The methodology is mainly designed to provide referential solutions in analyses of the numerical method called SubIval (the subinterval-based method for computation of the fractional derivative in initial value problems).

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Section: Motivationmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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“…To correct this deficiency, two fractional derivatives in the Caputo and Riemann-Liouville sense were defined by Atangana-Baleanu [45], based on the generalized stretched Mittag-Le er function. These new derivatives have been applied to different systems in [46][47][48].…”

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confidence: 99%

Analysis of Drude model using fractional derivatives without singular kernels

et al. 2017

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Abstract:We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Le er function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when < 0.8.

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“…The derivatives based on exponential appear naturally in many problems in nature as being able to describe the effect of fading memory. This class of derivative has been applied in several research papers for instance [5,7,13,15,16,[18][19][20]22]. However, it was noted by several experts in the field that, this new derivative does not have a non-local kernel as its corresponding integral is not fractional, thus a new kernel was suggested by Atangana and Baleanu [6] where after some manipulations, the exponential decay kernel was replaced by the generalized Mittag-Leffler kernel.…”

Section: Introductionmentioning

confidence: 99%

Analysis of rubella disease model with non-local and non-singular fractional derivatives

Koca

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this we extend the model describing the Rubella spread by changing the derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.

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Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

Cited by 99 publications

References 28 publications

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Analysis of Drude model using fractional derivatives without singular kernels

Analysis of rubella disease model with non-local and non-singular fractional derivatives

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