Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense

This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

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“…Then, the fractional conformable derivative of β-type in the Riemann-Liouville sense (AR) is given by [37] AR β…”

Section: γ(α)mentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

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“…Additionally, the computing burden when using this operator is considerably lighter than when using other fractional derivative definitions. All these features have been corroborated in the literature, where there have been a large number of works carried out with this definition [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 52%

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

2020

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This article studies the entropy generation of a mass-spring-damper mechanical system, under the conformable fractional operator definition. We perform several simulations by varying the fractional order γ and the damping ratio ζ , including the usual dynamic response when γ = 1.0 and the typical damping cases. We analyze the entropy production for this system and its strong dependency on both γ and ζ parameters. Therefore, we determine their optimal values to obtain the highest efficiency of the MSD response, as well as other impressive features.

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“…This fractional conformable derivative has been applied for modeling problems in different fields such as science, technology, and engineering with excellent results. ()…”

Section: Resultsmentioning

confidence: 99%

Determination of supercapacitor parameters based on fractional differential equations

Hidalgo‐Reyes

Gómez‐Aguilar

Escobar-Jiménez

et al. 2019

Circuit Theory & Apps

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In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions. KEYWORDS exponential decay-law, fractional calculus, fractional conformable derivative, Mittag-Leffler function, power-law, supercapacitor model Int J Circ Theor Appl. 2019;47:1225-1253.wileyonlinelibrary.com/journal/cta

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Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense

Cited by 84 publications

References 34 publications

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

Determination of supercapacitor parameters based on fractional differential equations

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