Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Carreño, C. A.; Rosales, J. J.; Merchan, L. R.; García, José Merced Lozano; Godínez, F. A.

doi:10.1002/cta.2677

Cited by 13 publications

(21 citation statements)

References 26 publications

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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: Introductionsupporting

confidence: 55%

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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Section: Introductionsupporting

confidence: 55%

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

2020

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“…Since the fractional derivative has been interpreted in the modified Riemann-Liouville sense, we have B(y(0), 0)y(0)]dτ. (38) For solving (36) in a numerical manner, the nonlinear transformation has also been applied. As a result, we have…”

Section: E Novel Simplestmentioning

confidence: 99%

“…1A, and x(0) � 0.2. We also assume that α � 0.9 and σ � 1 sec and numerically solve (36). By using the obtained solutions and keeping the above relationship between y(t) and Y(ξ) along with that of ξ and t mentioned above in mind, the phase portraits of x(t), i L (t), and v C (t) can be simulated as depicted in Figures 19-21, where the strange attractors can be observed.…”

Section: E Novel Simplestmentioning

confidence: 99%

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On the Dimensional Consistency Aware Fractional Domain Generalization of Simplest Chaotic Circuits

Banchuin

2020

Mathematical Problems in Engineering

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In this research, we generalize the simplest Chua’s chaotic circuit which is even more simpler than the four-element Chua’s circuit in terms of number of elements and the novel simplest chaotic circuit in the fractional domain by using the fractional circuit elements. Unlike the previous works, the time dimensional consistency aware generalization has been performed for the first time in this work. The dynamics of the generalized fractional nonlinear circuits have been analyzed by means of the fractional calculus based on the modified Riemann–Liouville fractional derivative where the Lyapunov exponents and dimensions have also been numerically calculated. We have found that including the dimensional consistency significantly alters the dynamic of the obtained fractional domain Chua’s circuit from that of the previous dimensional consistency ignored counterpart as different Lyapunov exponents and dimensions can be obtained. The conditions for both fractional domain circuits which cease to be chaotic have also been determined where such condition of Chua's circuit presented in this study is different from that of the previous work. This is because the time dimensionalconsistency has been included. The dynamical analyses of these circuits have also been performed where their conditions for being nonchaotic have been verified. Moreover, their emulators have also been realized.

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“…Later on, Carreño et al and Hidalgo‐Reyes et al studied the mathematical model of SCs independently through multiple derivative definitions. They used experimental data from various devices and a fitting process powered, respectively, by the traditional interior‐point method and the particle swarm optimisation algorithm 20,21 . They determined that formula based on the conformable and ABC operators are the excellent descriptors for capacitances between 1 F and 100 F.…”

Section: Introductionmentioning

confidence: 99%

Determination of a physically correct fractional‐order model for electrolytic computer‐grade capacitors

Cruz–Duarte

Manuel

Rosales

et al. 2020

Math Methods in App Sciences

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Electrolytic computer‐grade capacitors (ECGCs) are vastly implemented in energy storage systems. However, their models are not accurate and simple as other kinds of capacitors. For example, ECGCs and supercapacitors share many characteristics but have some differences because of their physicochemical properties, so it is wrong to assume their electrical behaviour is equivalent. In this work, we study the discharging response of ECGCs using four models obtained from fractional differential equations (FDEs) with integer initial conditions and causal fractional definitions, that is, Caputo and conformable operators. We also recall a correct procedure to achieve models from FDEs with physical consistency of units and avoiding additional and senseless constants. Thence, we perform a fitting procedure over an experimental dataset from six ECGCs via a hybrid solving procedure powered by the cuckoo search algorithm and interior‐point algorithm. Our results show that models based on the traditional ordinary differential equation give the worst description of discharge, while models containing the Mittag–Leffler function, with time to the power of fractional order as the argument, render the best description of ECGCs.

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Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Cited by 13 publications

References 26 publications

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

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

On the Dimensional Consistency Aware Fractional Domain Generalization of Simplest Chaotic Circuits

Determination of a physically correct fractional‐order model for electrolytic computer‐grade capacitors

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