Fractional-order autonomous circuits with order larger than one

Jiang, Yanwei; Zhang, Bo; Shu, Xujian; Wei, Zhihao

doi:10.1016/j.jare.2020.05.005

Cited by 29 publications

(21 citation statements)

References 34 publications

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“…(a) Proles of current for small time. and corresponding time proles are shown in Figure 2, along with the responses of the classical and integer order hereditary RC circuits, see (19) and (20), that are calculated by:…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Models of supercapacitor and ultracapacitor range from the linear constitutive equations obtained by combining resistors and fractional capacitors as in [7,26,27] to non-linear models like the one proposed in [9]. Moreover, fractional models of capacitor having the dierentiation orders exceeding the rst order are considered in [19], along with their behavior as circuit elements. Fractional order elements nd their application in the study of complex electric networks as well, see [34,43].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

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Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Using an appropriate circuit model to fit the experimental data, the obtaining parameters' values are further analyzed for the pain-no pain situations. Recent works also discuss fractional-order circuits in various forms [42][43][44][45].…”

Section: Bioimpedance Modelingmentioning

confidence: 99%

Bioimpedance Sensor and Methodology for Acute Pain Monitoring

Ghita

Neckebroek

Juchem

et al. 2020

Sensors

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The paper aims to revive the interest in bioimpedance analysis for pain studies in communicating and non-communicating (anesthetized) individuals for monitoring purpose. The plea for exploitation of full potential offered by the complex (bio)impedance measurement is emphasized through theoretical and experimental analysis. A non-invasive, low-cost reliable sensor to measure skin impedance is designed with off-the-shelf components. This is a second generation prototype for pain detection, quantification, and modeling, with the objective to be used in fully anesthetized patients undergoing surgery. The 2D and 3D time–frequency, multi-frequency evaluation of impedance data is based on broadly available signal processing tools. Furthermore, fractional-order impedance models are implied to provide an indication of change in tissue dynamics correlated with absence/presence of nociceptor stimulation. The unique features of the proposed sensor enhancements are described and illustrated here based on mechanical and thermal tests and further reinforced with previous studies from our first generation prototype.

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“…It was noticed that time-fractional derivatives usually appear as infinitesimal generators of the time evolution when choosing a long-time scaling limit. Several essential phenomena in physics and polymer technology [2], electrical circuits [3], electrochemistry [4], electrodynamics of complex medium [5], control theory [6], thermodynamics [7], viscoelasticity [8], aerodynamics [9], capacitor theory [10], biology [11], blood flow [12], and fitting of experimental data [13], are well described by the aforesaid equations. Equation (1) can be converted to time-fractional derivative of order α ∈ ð0, 1, as given by:…”

Section: Introductionmentioning

confidence: 99%

A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation

Ali

Nia

Rabiei

et al. 2021

Advances in Mathematical Physics

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In this manuscript, a semianalytical solution of the time-fractional Navier-Stokes equation under Caputo fractional derivatives using Optimal Homotopy Asymptotic Method (OHAM) is proposed. The above-mentioned technique produces an accurate approximation of the desired solutions and hence is known as the semianalytical approach. The main advantage of OHAM is that it does not require any small perturbations, linearization, or discretization and many reductions of the computations. Here, the proposed approach’s reliability and efficiency are demonstrated by two applications of one-dimensional motion of a viscous fluid in a tube governed by the flow field by converting them to time-fractional Navier-Stokes equations in cylindrical coordinates using fractional derivatives in the sense of Caputo. For the first problem, OHAM provides the exact solution, and for the second problem, it performs a highly accurate numerical approximation of the solution compare with the exact solution. The presented simulation results of OHAM comparison with analytical and numerical approaches reveal that the method is an efficient technique to simulate the solution of time-fractional types of Navier-Stokes equation.

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Fractional-order autonomous circuits with order larger than one

Cited by 29 publications

References 34 publications

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Bioimpedance Sensor and Methodology for Acute Pain Monitoring

A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation

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Fractional-order autonomous circuits with order larger than one

Cited by 29 publications

References 34 publications

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

Bioimpedance Sensor and Methodology for Acute Pain Monitoring

A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation

Contact Info

Product

Resources

About

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits